Question

The line ab has midpoint (-2, 4) a has coordinates (3, -2) find the coordinates of b

Answer 1

b = (- 7, 10 )

Explanation:

Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[
`(1)/(2)` (x₁ + x₂ ),
`(1)/(2)` (y₁ + y₂ ) ]

let the coordinates of b = (x, y ) then use the formula and equate to the coordinates of the midpoint, that is

`(1)/(2)` (x + 3) = - 2 ( multiply both sides by 2 )

x + 3 = - 4 ( subtract 3 from both sides )

x = - 7

`(1)/(2)` (y - 2) = 4 ( multiply both sides by 2 )

y - 2 = 8 ( add 2 to both sides )

y = 10

Thus the coordinates of b are (- 7, 10 )