Question

6.3.12
The coordinates of point T are (0,5). The midpoint of ST is (2,-2). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)

Answer 1

Answer:

$S = (4,-9)$

Step-by-step explanation:

Given

$T = (0,5)$

$Midpoint = (2,-2)$

Required

Find S

Midpoint is calculated as:

$Midpoint = 0.5(x_1 + x_2,y_1+y_2)$

So, we have:

$(2,-2)= 0.5(0+ x_2,5+y_2)$

Where x2 and y2 are the coordinates of S

Multiply through by 2

$2 * (2,-2)= 2 * 0.5(0+ x_2,5+y_2)$

$(4,-4)= (0+ x_2,5+y_2)$

$(4,-4)= (x_2,5+y_2)$

By comparison:

$x_2 = 4$

$5 + y_2 = -4$

$y_2 = -4-5$

$y_2 = -9$

So:

$S = (4,-9)$