# 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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Expert Answers

lfryerda | Certified Educator

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

`S=((0+2a)/2,(0+2b)/2)=(a,b)`

Similarly, the mipoint of P and R is

`T=((0+2c)/2,(0+0)/2)=(c,0)`

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

`m={y_2-y_2}/{x_2-x_1}`

So the slope of QR is

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

`=-b/{c-a}`

The slope of ST is

`m_{ST}={0-b}/{c-a}`

`=-b/{c-a}`

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

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