Question

If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.

Answer 1

Explanation:

The formula to find the midpoint of a segment is

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))` and we have the midpoint and we also have a coordinate of (5, 4). Let's let x₁ = 5 and y₁ = 4. Filling in what we have:

`(2,1)=((5+x_1)/(2),(4+y_2)/(2))` and we'll deal with the x terms first. The x coordinate of the midpoint is 2, so:

`2=(5+x_2)/(2)` and multiply both sides by 2 to get rid of the denominator to get:

4 = 5 + x₂ so

x₂ = -1. Going on to the y coordinate. The y coordinate of the midpoint is 1, so:

`1=(4+y_2)/(2)` and again multiply both sides by 2 to get rid of the denominator to get:

2 = 4 + y₂ so

y₂ = -2

The coordinates of T are (-1, -2)