Question

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​

Answer 1

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 )

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