Question

Point M is the midpoint of segment AC. Point M is located at (25.5, 60.1) and point C is located at (18.3, 72.5). What is the location of Point A ?

Answer 1

`A = (32.7,47.7)`

Explanation:

Given

`M = (25.5,60.1)`

`C = (18.3,72.5)`

Required

Determine the coordinates of A

Midpoint is calculated as thus:

`M(x,y) = ((A_x + C_x)/(2), (A_y + C_y)/(2))`

Substitute the given values

`(25.5,60.1) = ((A_x + 18.3)/(2), (A_y + 72.5)/(2))`

Multiply through by 2

`2 * (25.5,60.1) = ((A_x + 18.3)/(2), (A_y + 72.5)/(2)) * 2`

`2 * (25.5,60.1) = (A_x + 18.3, A_y + 72.5)`

`(51,120.2) = (A_x + 18.3, A_y + 72.5)`

By comparison:

`A_x + 18.3 = 51`

`A_y + 72.5 = 120.2`

`A_x + 18.3 = 51`

`A_x = 51 - 18.3`

`A_x = 32.7`

`A_y + 72.5 = 120.2`

`A_y = 120.2 - 72.5`

`A_y = 47.7`

Hence:

`A = (32.7,47.7)`