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

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

`x_K=(x_H+x_L)/(2),\\ \\y_K=(y_H+y_L)/(2).`

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

`-9=(1+x_L)/(2),\\ \\3=(-7+y_L)/(2).`

Find the coordinates of point L:

`-9=(1+x_L)/(2)\Rightarrow 1+x_L=-18,\ x_L=-19;`

`3=(-7+y_L)/(2)\Rightarrow -7+y_L=6,\ y_L=13.`

Answer: L(-19,13)

Answer 2

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

Step-by-step explanation:

The mid point of the coordinates (a,b) and (c,d) is given by
`((a+c)/(2),(b+d)/(2))`

Here we have (a,b) = (1,-7) and
`((a+c)/(2),(b+d)/(2))` = (-9,3) , we need to find (c,d).

`(a+c)/(2) =-9\\ \\ 1+c=-18\\ \\ c=-19\\\\ (b+d)/(2) =3\\ \\ -7+d=6\\ \\ d=13`

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