Question

Explain in the box below how you know

Answer 1

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.

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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.