Question

If p(6, -2), q(-2, 8), r(-4, 3) and s(-9, y), find the value of y so that pq is perpendicular to rs.

A) y = 4
B) y = 3
C) y = 7
D) y = -1

Answer 1

To find the value of y so that pq is perpendicular to rs, we need to check if the slope of pq is the negative reciprocal of the slope of rs. By setting up an equation using the coordinates and the slope formula, we can solve for y to find that y = 4.

Step-by-step explanation:

To determine the value of y so that the line segment PQ is perpendicular to the line segment RS, we need to check if the slope of PQ is the negative reciprocal of the slope of RS. The formula for calculating slope is given by m = (y2 - y1) / (x2 - x1). Given the coordinates of P(6, -2), Q(-2, 8), R(-4, 3), and S(-9, y), and knowing that slopes of perpendicular lines are negative reciprocals, we can set up the equation: (8 - (-2)) / (-2 - 6) = (y - 3) / (-9 - (-4)). Simplifying the equation gives us 10 / -8 = (y - 3) / -5.

Cross-multiplying and simplifying further, we get -5(10) = -8(y - 3). Solving for y, we find y = 4.