Question

What are the coordinates of Y if the midpoint of line segment XY is (2,-5) and the coordinates of point X is (4,4)?

Answer 1

Y(0, - 14 )

Explanation:

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

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

Use the midpoint formula and equate corresponding parts to the coordinates of the given midpoint

let Y = (x, y ), then

`(1)/(2)` (4 + x) = 2 ( multiply both sides by 2 )

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

x = 0

and

`(1)/(2)` (4 + y ) = - 5 ( multiply both sides by 2 )

4 + y = - 10 ( subtract 4 from both sides )

y = - 14

Thus

coordinates of Y = (0, - 14 )