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

Answer:

Step-by-step explanation:

The formula to find the midpoint of a segment is

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

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

$2=\frac{5+x_2}{2}$ 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:

$1=\frac{4+y_2}{2}$ 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)