Use the distance formula to show that the two triangles on the coordinate plane are congruent
Answers
Answer:
Step-by-step explanation:
d = [tex]\sqrt{(x_{2} -x_{1} )^2 + (y_{2} - y_{1} )^2}[/tex]
A(- 5, - 2) , B( - 1, - 6) , C ( - 9, - 6)
AB = √[(- 5 + 1)² + (- 2 + 6)²] = 4√2
BC = √[(- 1 + 9)² + (- 6 + 6)²] = 8
AC = √[(- 5 + 9)² + (- 2 + 6)²] = 4√2
D(2, 2) , E(6, - 2) , F( 10, 2)
DE = √[(2 - 6)² + (2 + 2)²] = 4√2
EF = √[(6 - 10)² + (- 2 - 2)²] = 4√2
DF = √[(2 - 10)² + (2 - 2)²] = 8
ΔABC ≅ ΔEDF
The two triangles ABC and DEF are not congruent by SSS.
What is the distance formula between two points?The distance formula between two points is,
[tex]D = \sqrt{(x_2 - x_1_)^2 + (y_2 - y_1)^2[/tex].
Two triangles will be congruent by SSS is the distance of their corresponding sides are equal.
In ΔABC coordinates of A and B are (-5, - 2) and (-1, - 6).
[tex]D_{AB} = \sqrt{(- 1 + 5)^2 + (- 6 + 2)^2}[/tex].
[tex]D_{AB} = \sqrt{(4)^2 + (-4)^2[/tex].
[tex]D_{AB} = \sqrt{(16) + (16)[/tex].
[tex]D_{AB} = \sqrt{32}[/tex].
Similarly, the distance of DF in ΔDEF is [tex]\sqrt{64}[/tex].
hence AB ≠ DF so the triangles are not congruent.
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Related Questions
A path for a new city park will connect the park entrance to Main Street, as shown to the right. The path should be perpendicular to Main Street. What is an equation that represents the path?
Answers
Answer:
[tex] y = -\frac{1}{2}x + 3 [/tex]
Step-by-step explanation:
To create an equation in slope-intercept form, y = mx + b, for the path, we need to find slope (m) of the path, and also determine the y-intercept (b) of the path.
First, find the slope of the main street:
Using two points on the main street, (2, 3) and (3, 5),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 -x_1} = \frac{5 - 3}{3 - 2} = \frac{2}{1} = 2 [/tex]
Since the path would be perpendicular to the main street, therefore, the slope of the path would be the negative reciprocal of 2.
Thus, the slope of the path, m = -½.
The y-intercept of the path is the point at which the line of the path cuts across the y-axis.
The path intercepts the y-axis at y = 3. Therefore, the y-intercept (b) = 3.
Substitute m = -½, and b = 3 into [tex] y = mx + b [/tex].
✅The equation that represents the path would be:
[tex] y = -\frac{1}{2}x + 3 [/tex]
Answer:
its y=1/2x+4 lol the other guy was 1 off
Step-by-step explanation:
How many feet are there in 3 meters?
Hint: 1 m 3.3 ft
Round your answer to the nearest tenth.
Answers
Answer:
9.8
Step-by-step explanation:
Answer:
9.9
Step-by-step explanation:
A team of 5 students is chosen at random from 14 girls and 13 boys. Determine
in how many ways can the team be chosen if
a) there are no restrictions.
b) there must be more girls than boys.
Answers
Answer:
A)9687600
b)340704
Step-by-step explanation:
Candace bought 14 sacks of dog food to share equally among three dog shelters. How much dog food does each shelter get?
Answers
Answer:
4 sacks
Step-by-step explanation:
Please help it’s due
Answers
5 = 60
6 = 150
7 = 30
if you have any more questions let me know
nixon cuts 5/6 inch sections of wood to make a birdhouse roof . he cut 24 sections. how many inches did he cut
Answers
Answer: 20 inches
Step-by-step explanation: 5/6 x 24 = 20
Answer:20 Inches
Step-by-step explanation:
5/6in*24=20inches
(04.02 LC) The graph below shows the numbers of cups of apple juice that are mixed with different numbers of cups of lemon-lime soda to make servings of apple soda: What is the ratio of the number of cups of apple juice to the number of cups of lemon-lime soda? (5 points)
Answers
Answer:
Ratio of the number of cups of apple juice to the number of cups of lemon lime soda is 6 : 1
Step-by-step explanation:
From the graph attached,
Number of cups of apple juice (A) is proportional to the number of cups of lemon lime soda (L).
A ∝ L
A = kL
Here 'k' is the proportionality constant.
k = [tex]\frac{A}{L}[/tex]
= [tex]\frac{6}{1}[/tex]
Therefore, ratio of the number of cups of apple juice to the number of cups of lemon lime soda is 6 : 1.
f(x)=2^x+1 and g(x)= f (x-3)
Enter the rule of function for g in the box
g (x) =
Answers
1 ball of wool is 125m, how many balls are there with 604m??
Answers
Answer:
4.8 balls of wool
Step-by-step explanation:
604÷125=4.8
A small order of fries at Wendy’s has 90 more calories than the small order of fries at McDonald’s. If together they have 550 calories, how many calories are in the Wendy’s small order of fries?
Answers
Answer:
320 caloriesStep-by-step explanation:
Small order of fries at Wendy’s = x calories
Small order of fries at McDonald’s = y calories
x = y + 90x + y = 550Substitute x in the second equation
y + 90 + y = 5502y = 550 - 902y = 460y = 230Then, x is:
x = 230 + 90 = 320 calories8.162 be when round to hundred place
Answers
Explanation: the 2 is less than five so it stays the same
I don't know if you mean rounding to the HUNDRED place or the HUNDREDTHS place, but I will give you both answers.
8.162 rounded to the hundreds place - 0
8.162 rounded to the HUNDREDTHS place- 8.16
What’s the answer for r
Answers
Answer:
can you show a picture :)
3n = –8 + 4n
with work shown
Answers
Answer:
n=8
Step-by-step explanation:
3n=−8+4n
Simplify both sides of the equation.
3n=4n−8 (there isn't so It stays the same.
Subtract 4n from both sides.
3n−4n=4n−8−4n
−n=−8
Divide both sides by -1.
−n/-1 =−8/-1
Answer:
n=8
Will give brainliest if u help!!! Thank you!
Answers
HELPPPP PLEASEEE ASAPPPPP
Answers
Answer:
Step-by-step explanation:
PQRS
PQ + QR + RS + PS = 186
RS = SP - 7
PQ = RS = x - 7
QR = PS = x
2x + 2(x - 7) = 186
4x = 200
x = 50
PQ and RS = 43
QR and SP are 50
what is x?
6-4x=6x-8x-2
Answers
Answer:
x=4
Step-by-step explanation:
isolate the variable (x) by dividing each side by the factors that don't contain the variable
ANSWER PLEASE !!!!! I NEED IT NOW!!
Answers
What are 25 times by the same number then divide it by sixty
Answers
625/60 ≈ 10.4166
Or when rounded to the nearest hundredth, 10.42
sove
[tex]2x - 5 = 7[/tex]
Answers
Answer:
X=6
Step-by-step explanation:
you add 5 on ther side, then add 7, and 5 together. then divide 2 on the other side
Answer:
x=6
Step-by-step explanation:
2x-5=7
add 5 on both sides:
2x-5+5=7+5
2x=12
Divide by 2:
x=6
Hope this helps!
The length of a rectangle is four times its width. Twice the perimeter of that rectangle is 160 cm. Find
the length and width of that rectangle. pls answer fast
Answers
Answer:
Step-by-step explanation:
Given twice the perimeter of rectangle =160
Let width of the rectangle=X
So length of the rectangle =4x
2(perimeter of rectangle)=160
2[2(length+width)]=160
4(4x+x)=160
5x=160/4
5x=40
X=40/8
X=5cm
So length of the rectangle =4x
=20cm
Width of the rectangle =X
=5cm.
Length = 4*5 = 20 cm
Width. = 4 cm.
rewrite 8x8x8 using an exponent
Answers
The exponential form of the given number 8x8x8 is 8³.
What is exponential form?The exponential form is a way of writing numbers using bases and powers. It tells us how many times are we actually multiplying a number to get the result.
Given is a number, 8x8x8,
As we know,
a×a×a××a×a×a×a×a×a...... n times = aⁿ
The number 8 is multiplied by itself 3 times, so, it will have a power of 3,
Therefore, 8x8x8 = 8³
Hence, the exponential form of the given number 8x8x8 is 8³.
Learn more about exponential form, click;
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What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
Answers
Answer:its b
Step-by-step explanation:
edge 2020
Answer:its b
Step-by-step explanation:
A developer has 7 1/2 acres of land to build houses on. If each house is to be built on -1/4 acre plot, how many houses can he build?
a 3
b 5
c 30
d 35
Answers
The value of the 8 in 89.945 is how many times rhe value of the 8 in 763.186
Answers
Answer:
1000x
Step-by-step explanation:
HELP ME PLZZZZZZZZZZ I WILL GIVE MORE POINTS AT THE END
Answers
Answer: the answer is u [tex]\geq[/tex] 2
What is 65658 divided by 706? SHOW YOUR WORK!!
Answers
Answer:
the answer is 93
Step-by-step explanation:
i dont know how to explain it but just use a calculator.
The library charged Monica $50 for a book that was 10 days overdue
Answers
4 cups 6 fl oz - 2 cups 7 fl oz
Answers
Answer:
What's the question?
Step-by-step explanation:
Put it DB and I'll gladly answer!
Is this linear regression equation a good fit for the data? Why or why not? A. r = - .7622 , so this is a good negative correlation fit for the data . B. r = - .9919 , so this is a very good negative correlation fit for the data C. r = .9919 , so this is a very good positive correlation fit for the data . D. r = .7622 so this is a good positive correlation fit for the data .
Answers
Answer: Is this linear regression equation a good fit for the data? Why or why not? A. r = - .7622 , so this is a good negative correlation fit for the data . B. r = - .9919 , so this is a very good negative correlation fit for the data C. r = .9919 , so this is a very good positive correlation fit for the data . D. r = .7622 so this is a good positive correlation fit for the data .
Step-by-step explanation:
Please i need help
A point on a wheel has a constant angular velocity of 3 rad/s. The angle turned through in 15 seconds is:
45 rad
10π
5 rad
90π rad
Answers
I think 10
Hope this help