Is The Line Through P(10, -9) and Q(12, -15) Perpendicular to The Line Through Points R(-8, 9) and S(-14, 7)? Explain.

Question

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Answer 1

If 2 lines are perpendicular then their slope are the negative reciprocal of one another. In other words if the slope of the first line is y/x then the slope of the perpendicular is -x/y . Their product will equal -1

the slope of the first line is -15 -(-9)/12-10= -6/2= -3

the slope of the second line is 9-7/-8-(-14) 2/6 = 1/3

The slopes are negative reciprocals and their product id -1 so yes they are perpendicular to one another

Answer 2

to be perpendicular the 2 lines must have slopes that are negative inverses of each other

PQ slope is -6/2= -3

RS slope is 2/6 = 1/3

they're negative inverses, so the lines are perpendicular

take the difference in y coordinates and divide by the difference in x coordinates to get slope, "rise over run"

vertical change divided by horizontal change. For PQ it's -15 - -9 all over 12-10, -15+9 = -6 over 2 = -3

do the same with RS find the change in y values, divide by change in x values