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. q ? p = 7 b. p ? q = 7 c. p q = 7 d. -q ? p = 7

Answer 1

The equation that correctly relates the coordinates p and q is p + q = 7.

Step-by-step explanation:

The equation that correctly relates the coordinates p and q is p + q = 7.

Since line AB is perpendicular to line BC, the slopes of the lines are negative reciprocals of each other. The slope of AB is (1-4)/(6-p) = -3/(6-p), and the slope of BC is (q-1)/(9-6) = (q-1)/3. As the product of the slopes of perpendicular lines is -1, we have (-3/(6-p))((q-1)/3) = -1. Simplifying, we get (6-p)(q-1) = -3. Expanding the equation gives 6q-p-6 = -3, which rearranges to p + q = 7.

Answer 2

To find the relationship between p and q for perpendicular lines AB and BC, we use the concept of negative reciprocal slopes. The slopes of AB and BC, based on their coordinates, lead us to the equation p + 3q = 9 which relates p and q.

Step-by-step explanation:

The question is asking to find the relationship between the coordinates p and q for points A and C given that lines AB and BC are perpendicular. We can find the slopes of these lines using the coordinates provided. For line AB, the slope is given by (1 - 4) / (6 - p) and for line BC, the slope is (q - 1) / (9 - 6). Since AB is perpendicular to BC, the product of their slopes should be equal to -1 (negative reciprocal).

Let's calculate:

The slope of AB: (1 - 4) / (6 - p) = -3 / (6 - p)

The slope of BC: (q - 1) / (9 - 6) = (q - 1) / 3

Product of slopes: (-3 / (6 - p)) * ((q - 1) / 3) = -1

Now we solve for p and q:

-3(q - 1) / (6 - p) = -1 * 3
3(q - 1) = 6 - p
3q - 3 = 6 - p
p + 3q = 9
p + 3q - 9 = 0

By rearranging terms we find that the correct relationship between p and q is p + 3q = 9.