Question

The coordinates of a, b, and c in the diagram are a(p,4), b(6,1), and c(9,q). which equation correctly relates p and q? hint: since is perpendicular to , the slope of � the slope of = -1. the coordinates of a, b, and c are in the diagram. ab and bc intersect at point b are 90 degrees. a. p q = 7 b. q ? p = 7 c. p ? q = 7 d. -q ? p = 7

Answer 1

To find the equation relating p and q, we use the fact that AB is perpendicular to BC and the slopes are negative reciprocals. By setting the slopes equal to their negative reciprocals, we can solve for p and q.

Step-by-step explanation:

To find the equation that relates p and q, we need to use the information given in the question. Since line AB is perpendicular to line BC, the slope of AB is the negative reciprocal of the slope of BC.

The slope of AB can be calculated as:

slope AB = (q - 4)/(p - 6)

And the slope of BC can be calculated as:

slope BC = (q - 1)/(9 - p)

Setting these two slopes equal to their negative reciprocals, we get:

(q - 4)/(p - 6) = -1/((q - 1)/(9 - p))

Simplifying this equation will give us the relation between p and q.

Answer 2

To solve this problem, we need to use the fact that lines AB and BC are perpendicular, which means the slopes of these lines are negative reciprocals of each other. This implies that the product of the slopes must equal -1. The equation that correctly relates p and q is p + q = 7.

Let's find the slopes of AB and BC first.

The slope of a line is calculated by the formula (change in y) / (change in x), which we can denote as (delta y) / (delta x).

For line AB, points A and B have coordinates A(p, 4) and B(6, 1), respectively.

Slope of AB = (delta y) / (delta x)
= (1 - 4) / (6 - p)
= (-3) / (6 - p)

For line BC, points B and C have coordinates B(6, 1) and C(9, q), respectively.

Slope of BC = (delta y) / (delta x)
= (q - 1) / (9 - 6)
= (q - 1) / 3

Now, as AB is perpendicular to BC, their slopes' product should be -1.

Therefore,
Slope of AB × Slope of BC = -1
(-3)/(6 - p) × (q - 1)/3 = -1

Simplifying this expression, we cancel out the 3s:
(-1)/(6 - p) × (q - 1) = -1

Cross-multiplying yields:
-q + 1 = -6 + p

Now, we can rearrange the terms to isolate the variables p and q on one side:
q + p = 7

This equation matches option (a), which is the correct equation that relates p and q based on the condition that the lines AB and BC are perpendicular.