C is the midpoint of PQ, if P is (4,m) , C is (n,-1) and Q is (-2,4) then m & n respectively are
Answers
Given points are P(4,m) and Q(-2,4)
Let (x1, y1) = P(4,m)
Where, • x1 = 4 and • y1 = m
Let (x2, y2) = Q(-2,4)
Where, • x2 = -2 and • y2 = 4
We know that
The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)
is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )
Mid point of the linesegment PQ
⇛M(x,y) = ( { 4+(-2)}/2 ,{m+4}/2)
⇛M(x,y) = {(4-2)/2 , {m+4}/2)
⇛M(x,y) = (2/2,{m+4}/2)
⇛M(x,y) = (1,{m+4}/2)
According to the given problem
Mid point of PQ = C(n,-1)
M(x,y) = C(n,-1)
(1,{m+4}/2) = (n,-1)
On Comparing both sides then
1 = n and (m+4)/2 = -1
n = 1 and m+4 = -2
n = 1 and m = -2-4
n = 1 and m = -6
Hence, the value of m&n will be (1&-6) respectively.
Additional comment:
The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)
is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )
also read similar questions: Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following pr...
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