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  parallel lines both have slope 1/3; non-parallel lines both have length 5

Step-by-step explanation:

It generally works well to follow instructions.

A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...

  A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)

So, the slope of RA is Δy/Δx = 3/9 = 1/3

And the other difference and slope are ...

  P -T = (9, 4) -(-3, 0) = (12, 4)   ⇒   Δy/Δx = 4/12 = 1/3

The slope of RA is the same as the slope of PT, so those segments are parallel.

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The length of segment TR can be found from the differences of the end point coordinates:

  R - T = (-3, 5) -(-3, 0) = (0, 5)

Since these points are on the same vertical line, this tells us the segment length is 5.

The other difference of coordinates is ...

  A - P = (6, 8) -(9, 4) = (-3, 4)

The distance formula tells us the length of AP is then ...

  AP = √((-3)² +4²) = √25 = 5

Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.

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step-by-step explanation: