Note that going from R to Q means we go down 3 and to the right 2. The slope here is -3/2. You can use the slope formula to get the same result. The slope formula is:
m = (y2-y1)/(x2-x1)
Using the visual trick or the slope formula, we see that the slope of QS is 2/3. We go up 2 and over to the right 3 to go from S to Q.
-------------------
In summary so far:
- slope of RQ = -3/2
- slope of QS = 2/3
If we multiply the slopes together, we end up with -1
(-3/2)(2/3) = (-3*2)/(2*3) = -6/6 = -1
Any time two slopes multiply to -1, this means the lines are perpendicular. Because we got -1 as a result, we have shown that segment RQ is perpendicular to segment QS. Angle RQS is 90 degrees.
