Question

Given P(9,-6, Q(0,3), R(2,-3), and S(x,-5).find x such that PQ ⊥ RS

Answer 1

To find x such that PQ is perpendicular to RS, we find the slopes of PQ and RS and equate them. Then we solve for x, which is found to be 0.

Step-by-step explanation:

To determine the value of x such that PQ is perpendicular to RS, we can use the concept of slopes.

First, we find the slope of the line PQ by using the formula:

slope of PQ = (y2 - y1) / (x2 - x1) = (-6 - 3) / (9 - 0) = -9/9 = -1

Since PQ is perpendicular to RS, the slope of RS will be the negative reciprocal of -1, which is 1.

Next, we find the slope-intercept form of the line RS using the point (2, -3) and the slope 1:

y - y1 = m(x - x1)

y - (-3) = 1(x - 2)

y + 3 = x - 2

y = x - 5

Finally, we can substitute the value of x in the equation y = x - 5 with the y-coordinate of point S (-5), and solve for x:

-5 = x - 5

x = 0

Therefore, the value of x that makes PQ perpendicular to RS is x = 0.