Question

K is the midpoint of segment HL . H has coordinates (1, -7 ) , and K has coordinates(-9, 3 ). Find the coordinates of other end point L.

Answer 1

Answer:

Coordinates of other end point L = ( -19, 13 )

Explanation:

 The mid point of the coordinates (a,b) and (c,d) is given by $(\frac{a+c}{2},\frac{b+d}{2})$

 Here we have (a,b) = (1,-7) and $(\frac{a+c}{2},\frac{b+d}{2})$ = (-9,3) , we need to find (c,d).

 $\frac{a+c}{2} =-9\\ \\ 1+c=-18\\ \\ c=-19\\\\ \frac{b+d}{2} =3\\ \\ -7+d=6\\ \\ d=13$

So coordinates of other end point L = ( -19, 13 )

Answer 2

If K is midpoint of segment HL, then its coordinates can be calculated by the formula

$x_K=\dfrac{x_H+x_L}{2},\\ \\y_K=\dfrac{y_H+y_L}{2}.$

You are given coordinates of points H and K: H(1,-7) and K(-9,3), then

$-9=\dfrac{1+x_L}{2},\\ \\3=\dfrac{-7+y_L}{2}.$

Find the coordinates of point L:

$-9=\dfrac{1+x_L}{2}\Rightarrow 1+x_L=-18,\ x_L=-19;$

$3=\dfrac{-7+y_L}{2}\Rightarrow -7+y_L=6,\ y_L=13.$

Answer: L(-19,13)