Question

One endpoint on GH is H(78.8, 4). The midpoint is M(43.3, 20). Find the coordinates of endpoint G.

O (7.8, 36)
O (59.3, -15.5)
O (61.05, 12)
O (114.3,-12)

Answer 1

first option

Explanation:

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

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

use this formula with (x₁, y₁ ) = G(x, y ) and (x₂, y₂ ) = H (78.8, 4 )

and equate to x/ y coordinates of midpoint , that is

`(x+78.8)/(2)` = 43.3 ( multiply both sides by 2 to clear the fraction )

x + 78.8 = 86.6 ( subtract 78.8 from both sides )

x = 7.8

and

`(y+4)/(2)` = 20 ( multiply both sides by 2 to clear the fraction )

y + 4 = 40 ( subtract 4 from both sides )

y = 36

the coordinates of G (7.8, 36 )