Given the coordinates, determine whether PQR & XYZ are congruent


P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)


PQ=

XY=

QR=

YZ=

PR=

XZ=


Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.

Answers

Answer 1

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)


Related Questions

Jordan found cloth for $7.50 per yard. How much would his total cost be if he needed 12 yards of cloth?

Answers

Jordan would need 90 dollars

What is the slope of the line that passes through
the points (-5, -5) and (6, – 9)?

Will give brainliest pls answer immediately!

Answers

Answer:

[tex]slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } \\ = \frac{( - 9 - ( - 5))}{(6 - ( - 5))} \\ = \frac{ - 4}{11} \\ slope = - \frac{4}{11} [/tex]

A=
B=
Blank 1:
Blank2:

Answers

Answer:

a=3,b=1

Step-by-step explanation:

In a parallelogram opposite sides are equal/congruent.

Using this, we know that 3a-4=a+2 and b+1=2b

1st equation:

3a-4=a+2

-a       -a

2a-4=2

   +4 +4

2a=6

a=3

2nd equation:

b+1=2b

-b     -b

b=1

a=3, b=1

Which expression would be easier to simplify if you used the associative property to change the grouping?
A.(160+40)+27(160+40)+27

B.0.85+[0.15+(-\frac{1}{3})]0.85+[0.15+(− 31 )]

C.[(-\frac{1}{3})+(-\frac{2}{3})]+(-\frac{4}{5})[

D.1 + ( 3/4 + ( - 3/4)


brainliest if right and its on ap..ex

Answers

Answer:

C is the answer

Step-by-step explanation:

Somehow this was in my test last week , lol

Kim rols three 6 sided dice.
The product of her numbers is 60
a) What numbers could she have rolled?

Answers

Answer:

2,5,6

Step-by-step explanation:

2 * 5 * 6 = 60

Kim rolls three 6 sided dice.  The product of her numbers is 60. So, the numbers are 2, 5, and 6 and this can be determined by using arithmetic operations.

Given :

Kim rolls three 6 sided dice.The product of her numbers is 60.

The following steps can be used to determine the number could Kim has rolled:

Step 1 - Let the three numbers be a,b, and c.

Step 2 - Given that the product of these numbers is 60.

[tex]a\times b \times c = 60[/tex]

Step 3 - So, the possible values of a, b, and c are:

a = 2

b = 5

c = 6

Step 4 - Check the product of a, b, and c if it is 60 then it is correct.

[tex]2\times 5\times 6 = 60[/tex]

For more information, refer to the link given below:

https://brainly.com/question/13101306

16 – (3 – 4y) = 2(y + 2)

Answers

Answer:

[tex]y = -4\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]16-(3-4y) = 2(y+2)[/tex]

Distribute.

[tex]16 - 3 + 4y = 2y + 4[/tex]

Combine like terms.

[tex]13 + 4y = 2y + 4[/tex]

Subtract [tex]2y[/tex] from both sides.

[tex]13 + 2y = 4[/tex]

Subtract 13 from both sides.

[tex]2y = -9[/tex]

Divide both sides by 2.

[tex]y = -4\frac{1}{2}[/tex]

I hope this helps!

To catch a ball, a professional baseball player leaps into the air with an initial velocity of
14 feet per second. Write a model for the height of the player above the ground after t seconds. After how many seconds does the player land on the ground? What would be the domain of this function?

Answers

Answer:

The answer is below

Step-by-step explanation:

a) The baseball player leaps into the air with an initial velocity of  14 feet per second. This means that the player leaps from the ground, the initial height is therefore zero.

The height (y) is given by the formula:

y(t) = ut - (1/2)gt² + initial heigth

u = initial velocity = 14 ft/s, t = time taken, g = acceleration due to gravity = 32 ft/s². Substituting:

y(t) = 14t - (1/2) * 32 *t² + 0

y(t) = 14t - 16t²

b) when the player is on the ground, the height = 0. hence:

0 = 14t - 16t²

16t² - 14t = 0

t(16t - 14) = 0

t = 0 or 16t - 14 = 0

t = 0 or 16t = 14

t =0 or t = 0.875

Hence t = 0.875 seconds

c) The domain is the set of possible values for the time. Hence:

Domain = (0, 0.875] = 0 < t ≤ 0.875

A coin contains 9 grams of nickel and 16 grams of Copper, for a total of 25 grams. What percentage of the metal is copper?

Answers

Answer:

The copper percentage = 64%

Step-by-step explanation:

Given

Nickle quantity = 9 grams of nickelCopper quantity = 16 grams of nickelTotal quantity = 25 grams

The percentage of copper metal can be determined using the formula

Copper percentage = [Copper quantity / Total quantity] × 100

                                  = [16 / 25] × 100

                                   = 0.64 × 100

                                   = 64%

Therefore, the copper percentage = 64%

If there were 1,593 Ronald McDonald's in the McDonald's, how many could fit?

Answers

depends on the size of the mcdonald’s

Answer:

over 1,593

Step-by-step explanation:

if there was already 1,593 Ronalds in the McDonalds the McDonalds can most likely fit over that amount

-5/12 - (-9/3)=

Help me please

Answers

Answer:

HOW T.F DO YOU NOT

Step-by-step explanation:

-5/12+3

2 7/12

UST CAUSE

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Step-by-step explanation:

PLEASE ANSWER GIVING 30 POINTS

Answers

Answer:

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Step-by-step explanation:

answer: D)

Answer:

The answer should be 15.

Step-by-step explanation:

[tex]\sqrt[3]{125}[/tex] Factor 125 = [tex]5^{2}[/tex] x 5. Rewrite the square root of the product [tex]\sqrt{5^{2}X5 }[/tex]  as the product of square roots. [tex]\sqrt{5^{2} }[/tex]   [tex]\sqrt{5}[/tex]. Take the square root of [tex]5^{2}[/tex].

[tex]3[/tex] x [tex]\sqrt[5]{5}[/tex] Multiply 3 and 5 to get 15.

[tex]\sqrt[15]{5}[/tex]

There are 23 students in a sixth-grade class. Nine students play hockey.
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O 9 to 23
O 14 to 23
O 14 to 9
O 9 to 14

Answers

Answer:

14:23

Step-by-step explanation:

14:23

Answer:

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Step-by-step explanation:

Look at pic and pls halp

Answers

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You are your friend are playing a game where you flip a coin and roll a fair four-sided die.

Answers

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Step-by-step explanation:

What is the quotient of 154,504 divided by 28

Answers

Answer:

5518

Step-by-step explanation:

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Y=9x-5

Answers

Answer:

liner

Step-by-step explanation:

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Answers

Answer:

π×8² =

201.0619298297

arc length formular = π ×r²

which expression is equivalent to 15+8x+3+2x​

Answers

Answer:

10x + 18

Step-by-step explanation:

First, we need to add like terms. Like terms are terms that are alike. For instance 8x and 2x are like terms. 15 and 3 are also like terms.

So, we have to add 8x plus 2x and 15 plus 3. That’s comes out to 10x plus 18.

Therefore, this expression is equivalent to 10x + 18.

Pythagorean Theorem Quiz.
1.) Find the unknown side length. Simplify answers that are radicals.
4
3
2.) Find the unknown side length. Simplify answers that are radicals.
16
12

Answers

Answer:

1.) 5              2.) 10.58

Step-by-step explanation:

For each one, you use the equation a^2 + b^2 = c^2 where c is the "hypotenuse"-- the side of the triangle opposite (facing) the right angle which is shown with a small box. The variables a and b do not matter, as long as they are the "legs", the other 2 sides.

So it is 4^2 + 3^2 = c^2 which simplifies to 16+9=25=c^2 and square root both sides and you get c=5

and 12^2 + b^2 = 16^2 which simplifies to 144+ b^2 = 256 and subtract 144 from both sides and you get b^2 = 112 and square root both sides and it is approximately 10.6 :)


Cheri uses her Tune-It-Up music card to make a $12 purchase of a few of her favorite songs. Which integer represents the effect of Cheri's purchase on the balance of her music card?

A) −$12
B) −$11
C) $0
D) $12

Answers

Answer:

Step-by-step explanation:

A, -12

if she had an x amount on her card,

after the buys the songs, she will have x-12 left

A, because she is using 12 dollars so it would minus 12 dollars

3 fifths equals how many 20

Answers

Answer:

12

Step-by-step explanation:

20/5 = 4

4 x 3= 12

3/5 of 20 is 12.

This is because 3/5*20/1=60/5 which reduces to 12.

Please Help ASAP!! ❤️ ​

Answers

Answer:

Step-by-step explanation:

*a is 6:55

*b is 37

*c is 15:12

a pack of 10 pair of socks cost 16.80. what is the cost for one pair of socks​

Answers

Answer:   $1.68 per pair of socks

Step-by-step explanation:

16.80- 10 = 1.68

Provide a radian measure of an angle that is 5/8 of a revolution counterclockwise from the x-axis.

Answers

I’m pretty sure but not so sure I think it is 180

The sum of three angle measures in a triangle is always 180°.

Answers

Answer:

YES IT IS RIGHT.......!

Markers were placed at altitudes of 10 and 15 feet below sea level Enter the integer that represents the altitude closer to sea level​

Answers

Answer:

43

neeed...20...charetors

The integer that represents the altitude closer to sea level​ is 10.

What is addition?

Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value. A numerical expression is algebraic information stated in the form of numbers and variables that are unknown.

We are informed that Markers were placed at altitudes of 10 and 15 feet below sea level

Then we need to find the integer that represents the altitude closer to sea level​.

We can say that 10 is negative (below the sea level), and 10 is 10 spaces away from zero on the number line, meaning the answer could be |10|.

The sea level would be 0 and the 10 would be -10 and the 15 will be -15

Hence, the 10 is closer to the sea level.

Thus the integer that represents the altitude closer to sea level​ is 10,

Learn more about fraction addition here:

https://brainly.com/question/17544795

#SPJ2

9. A cell phone can be purchased from the manufacturer for $160. The online retailer has a
standard markup of 30%, and the store has a standard markup of 40%.
(a)What is the price of the cell phone when purchased online?
(b)What is the price of the cell phone when purchased at the store?
(c) Which is the better deal?

Answers

Answer Below

30% of 160 is 48 dollars. Meaning you would take the 48 from 160. Leaving 112.So the 30% mark up would mean you would pay $112.Saving $48.

Take the 160 dollar,and have the 40% to work with. Taking this would be $64. So 160-64 is $96. They will spend $96 on the phone in-store

Purchase online- $112

Purchase in-store-$96

The better deal is in-store

Answer:

(A) $208   (B) 224   (C) the online one. it cost less

Step-by-step explanation:

(A) find 30% of $160 and add it to 160. put that answer in dollars.

(B) find 40% of $160 and add it to 160. put that answer in dollars.

(C) it is the one that costs less

Please help me with my delta math

Answers

Answer:

Use “ Math- way”

Step-by-step explanation:

It’s a web browser made for this stuff, you‘re welcome

Let T: P2 → P3 be the transformation that maps a polynomial p(t) into the polynomial (t-2)p(t).

a. Find the image of p(t) = 2-t + t^2
b. Show that T is a linear transformation.
c. Find the matrix for T relative to the bases (1, t,t^2) and (1,t,t^2,t^3).

Answers

(a) Applying T to p(t) = 2 - t + t ² gives

T ( p(t) ) = (t - 2) (2 - t + t ²) = -4 + 4t - 3t ² + t ³

(b) T is a linear transformation if for any p(t) and q(t) in P₂ and complex scalars a and b, the image of any linear combination of p and q is equal to the linear combination of the images of p and q. In other words,

T ( a p(t) + b q(t) ) = a T ( p(t) ) + b T ( q(t) )

Let

p(t) = α₀ + αt + αt ²

q(t) = β₀ + βt + βt ²

Compute the images of p and q :

T ( p(t) ) = (t - 2) (α₀ + αt + αt ²)

… = -2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + αt ³

Similarly,

T ( q(t) ) = -2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + βt ³

Then

a T ( p(t) ) + b T ( q(t) ) = a (-2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + αt ³) + b (-2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + βt ³)

… = c₀ + ct + ct ² + ct ³

where

c₀ = -2 (a α₀ + b β₀)

c₁ = a (α₀ - 2α₁) + b (β₀ - 2β₁)

c₂ = a (α₁ - 2α₂) + b (β₁ - 2β₂)

c₃ = a α₂ + b β

Computing the image of a p(t) + b q(t) would give the same result; just multiply it by t - 2 and expand. This establishes that T is indeed linear.

(c) Find the image of each vector in the basis for P₂ :

T (1) = (t - 2) × 1 = t - 2

T (t ) = (t - 2) t = t ² - 2t

T (t ²) = (t - 2) t ² = t ³ - 2t ²

Then

[tex]T=\begin{bmatrix}-2&0&0\\1&-2&0\\0&1&-2\\0&0&1\end{bmatrix}[/tex]

Indira is using a number line to add Negative 1 + (negative 3). She begins by showing –1 on the number line, as shown below.

A number line going from negative 5 to positive 5. The area between negative 1 and 0 is highlighted.

What is the sum of Negative 1 + (negative 3)?
–4
–3
2
3

Answers

Answer= -4

-1+-3=-4

Step by step-
Add like normal then add the sign since both numbers are negative.
3+1= 4 then add the sign

Answer:

-4

Step-by-step explanation:

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