Question

In the diagram below of triangle P, Q, RPQR, SS is the midpoint of start overline, P, R, end overline
PR
and TT is the midpoint of start overline, Q, R, end overline
QR
​
. If S, T, equals, minus, 1, plus, 4, xST=−1+4x, and P, Q, equals, 4, plus, 6, xPQ=4+6x, what is the measure of start overline, S, T, end overline
ST
?

Answer 1

Since SS is the midpoint of PR, we can set up the following equations:

PS = SR
ST = TR

By looking at the lengths of PS, SR, and ST, we can see that:

PS = 4 + 6x
SR = -1 + 4x
ST = -1 + 4x + 4 + 6x

Now, equating PS to SR:

4 + 6x = -1 + 4x
2x = -5
x = -2.5

Substitute x back into the expression for ST:

ST = -1 + 4(-2.5) + 4 + 6(-2.5)
ST = -1 - 10 + 4 - 15
ST = -22

Therefore, the measure of ST is 22.