+0  
 
0
707
2
avatar+46 

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
 #1
avatar+46 
+1

Any help? I think it is 5

Redsox123  May 11, 2017
edited by Redsox123  May 11, 2017
 #2
avatar+7339 
+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!! laugh

hectictar  May 11, 2017

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