Question

T is the midpoint of KL. K has coordinates (2,−6), and T has coordinates (−4,2). Identify the coordinates of L.

Answer 1

`L = (-10,10)`

Explanation:

Given

`K = (2,-6)`

`T = (-4,2)`

Required

Determine the coordinates of L

Since T is the midpoint of K and L, we make use of:

`T_x = (K_x + L_x)/(2)`

and

`T_y = (K_y + L_y)/(2)`

Solving for
`L_x`

`T_x = (K_x + L_x)/(2)`

`-4 = (2 + L_x)/(2)`

Multiply through by 2

`-8 = 2 + L_x`

`L_x = -8 - 2`

`L_x = -10`

Solving for
`L_y`

`T_y = (K_y + L_y)/(2)`

`2 = (-6+L_y)/(2)`

Multiply through by 2

`4 = -6 + L_y`

`L_y = 4 + 6`

`L_y = 10`

Hence: The coordinates of L is:

`L = (-10,10)`