Question

The points A, B and C have coordinates (5,1), (p,7) and (8,2) respectively.

Given that the distance between points A and B is twice the distance between points A and C, (7) calculate the possible values of p.

Answer 1

The possible values of p are p=11 or p=−4.

Let's solve the system of equations:

(5−p)^2 +(1−7)^2 =4(5−8)^2 +(1−2)^2 p=?

​We can solve the system of equations by expanding the squares and then combining like terms.

Steps to solve:

1. Expand the squares:

(5−p)^2 +(1−7)^2

=4(5−8) +(1−2)^2 25−10p+p^2 +36​=16+96+1 p^2 −10p+62 =113 p^2 −10p−51 =0

​2. Factor the quadratic:

(p−11)(p+4)=0

3. Solve for p:

p=11 or p=−4

Answer:

p=11 or p=−4