ABC is a triangle in which angle ABC = 90° p and q are integers such that the coordinates of A are (p, 10) the coordinates of B are (-1, -5) the coordinates of C are (8, q )

Question

ABC is a triangle in which angle ABC = 90°

p and q are integers such that

the coordinates of A are (p, 10)

the coordinates of B are (-1, -5)

the coordinates of C are (8, q )

Given that the gradient of AC is - 5/7

work out the value of p and the value of q

Answer 1

Since the slope of line AC is -5/7:

(10-q)/(p-8) = -5/7

Since angle B is a right angle, the product of the slopes of lines AB and BC must be -1.

15/(p+1) times (q+5)/ 9 = -1

That is two equations with two unknowns. At this point you have choices.

One possibility, solve each equation for q in terms of p, equate the results and solve for p. Once you have p, substitute that value into one of those equations to get q.

Try it yourself then check your work here:

desmos.com/calculator/pevufoqymf

Except the problem states p and q are integers which is contradicted by Desmos.