is the line through points p(-3,-2) and Q(2,3) perpendicular to the line through points R(10,-1) and S(15,-6)? explain.

Answer:B. Yes. Their slopes have product -1.Step-by-step explanation:Given: Line passing through P(-3, -2) and Q(2, 3)Line passing through R(10, -1) and S(15, -6)Required: To determine if both lines are perpendicular.SOLUTION:Two lines are considered perpendicular if the product of their slopes equal -1.To determine if both lines given in the question are perpendicular, first, calculate their slope using: [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]Slope of line passing through P(-3, -2) and Q(2, 3):Let,[tex] P(-3, -2) = (x_1, y_1) [/tex][tex] Q(2, 3) = (x_2, y_2) [/tex][tex] m = \frac{3 -(-2)}{2 -(-3)} [/tex][tex] m = \frac{5}{5} = 1 [/tex]Slope of line passing through R(10, -1) and S(15, -6):Let,[tex] R(10, -1) = (x_1, y_1) [/tex][tex] S(15, -6) = (x_2, y_2) [/tex][tex] m = \frac{-6 -(-1)}{15 - 10} [/tex][tex] m = \frac{-5}{5} = -1 [/tex]The product of their slopes = 1 × -1 = -1Therefore, the lines are perpendicular.The answer is: B. "Yes. Their slopes have product -1."