How to find a point if you have the midpoint

Asked by admin @ 29/10/2021 in Mathematics viewed by 308 People

Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T

Answered by admin @ 29/10/2021

Answer: The required co-ordinates of point T are (13, -6).

Step-by-step explanation: given that S is the midpoint of the line segment RT, where the co-ordinates of point R are (-9, 4) and that of S are (2, -1).

We are to find the co-ordinates of point T.

We know that

the co-ordinates of the mid-point of a line segment with endpoints (a, b) and (c, d) are given by

$\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).$

Let (h, k) be the co-ordinates of point T. Then, according to the given information, we have

$\left(\dfrac{-9+h}{2},\dfrac{4+k}{2}\right)=(2,-1)\\\\\\\Rightarrow \dfrac{-9+h}{2}=2\\\\\Rightarrow -9+h=4\\\\\Rightarrow h=4+9\\\\\Rightarrow h=13$

and

$\dfrac{4+k}{2}=-1\\\\\Rightarrow 4+k=-2\\\\\Rightarrow k=-2-4\\\\\Rightarrow k=-6.$

Thus, the required co-ordinates of point T are (13, -6).

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