Question

Q8
The midpoint of GH is M (2,2). One endpoint is H (1,9). Find the coordinates of endpoint G.

Answer 1

Answer:

(3,-5)

Step-by-step explanation:

Given

$M = (2,2)$

$H = (1,9)$

Required

Determine G

This is calculated using the following midpoint formula;

$M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

Where

$(x,y) = (2,2)$ and $(x_1,y_1) = (1,9)$

Substitute these values in the formula above

$(2,2) = (\frac{1 + x_2}{2},\frac{9 + y_2}{2})$

Solving for $x_2$

$2 =\frac{1 + x_2}{2}$

Multiply both sides by 2

$2 * 2 = 1 + x_2$

$4 = 1 + x_2$

$x_2 = 4 - 1$

$x_2 = 3$

Solving for $y_2$

$2 = \frac{9 + y_2}{2}$

Multiply both sides by 2

$2 * 2 = 9 + y_2$

$4 = 9 + y_2$

$y_2 = 4 - 9$

$y_2= -5$

Hence, the coordinates of G is $(3,-5)$