Find the coordinates of midpoint S of segment PQ and the midpoint T of segment PR. Then find the slope of segment QR and ST.   Thank you for your help.

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lfryerda | High School Teacher | (Level 2) Educator

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To find the midpoint of PQ and PR, we need to find the average of the endpoints of each line segment.

Since `P=(0,0)` and `Q=(2a,2b)` , then the midpoint is 


Similarly, the mipoint of P and R is


Now we find the slope of the two lines using the slope formula


So the slope of QR is

`m_{QR}={0-2b}/{2c-2a}`   factor 2 from numerator and denominator


The slope of ST is



so both slopes are the same and the lines are parallel.

The slope of QR and ST is `m=-b/{c-a}` .

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