Question

Find the coordinates of h if x(11, -6) is the midpoint of gh and g(15, 4).

Answer 1

h (7, - 16 )

Explanation:

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

M = (
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` ) ← midpoint formula

let the coordinates of h be (x, y )

here (x₁, y₁ ) = g (15, 4 ) and (x₂, y₂ ) = h (x, y )

use the midpoint formula on g, h and equate to the coordinates x (11, - 6 )

`(15+x)/(2)` = 11 ( multiply both sides by 2 )

15 + x = 22 ( subtract 15 from both sides )

x = 7

and

`(4+y)/(2)` = - 6 ( multiply both sides by 2 )

4 + y = - 12 ( subtract 4 from both sides )

y = - 16

then

coordinates of h = (7, - 16 )