Question

If one endpoint of a line segment is (2, 8) and the midpoint is (-4, 7), what is the other endpoint? (8, -5)

Answer 1

( - 10, - 22 )

using the midpoint formula,

let the other endpoint have coordinates (x, y) then

$\frac{1}{2}$ (2 + x ) = - 4 ( multiply through by 2 )

2 + x = - 8 ( subtract 2 from both sides ) then

x = -8 - 2 = - 10 ← value of x-coordinate

Similarly for y-coordinate

$\frac{1}{2}$ (8 + y ) = - 7 ( multiply through by 2 )

8 + y = - 14 ( subtract 8 from both sides )

y = - 14 - 8 = - 22 ← y -coordinate

the other endpoint is ( - 10, - 22 )