A triangle has vertices P(−7, 3), Q(1, 3), and R(1, −3). S is the midpoint of line segment PQ and T is the midpoint of line segment QR. What is the length of line segment ST?

A.) ST= 6 square root 2

B.) ST= 5

C.) ST= 3 square root 2

D.) ST= 4

Redsox123
May 11, 2017

#2**+2 **

**S** \(= \text{the midpoint of PQ} \\~\\ = \text{the midpoint of (-7, 3) and (1, 3)} \\~\\ = ( \frac{-7+1}2,\frac{3+3}{2}) \\~\\ = (-3, 3) \\~\\\)

**T** \(= \text{the midpoint of QR} \\~\\ = \text{the midpoint of (1, 3) and (1, -3)} \\~\\ = ( \frac{1+1}{2},\frac{3+-3}{2}) \\~\\ = (1, 0) \\~\\\)

**length of ST** \(=\sqrt{(-3-1)^2+(3-0)^2} \\~\\ =\sqrt{(-4)^2+(3)^2} \\~\\ =\sqrt{16+9} \\~\\ =\sqrt{25} \\~\\ =5\)

You got it right!!

hectictar
May 11, 2017