Question

The points A(-3p-3, 2p), B(-5p+1, 0) and C(0, 8p), where p is a constant are collinear. Find: the value of p​

Answer 1

• p = 5

Explanation:

Since all points are on same line, AB and BC have same slope.

Use slope formula and compare:

• m(AB) = (0 - 2p)/(-5p + 1 + 3p + 3) = -2p / (-2p + 4) = p/(p - 2)
• m(BC) = (8p - 0)/(0 + 5p - 1) = 8p / (5p - 1)
• m(AB) = m(BC)

Compare and solve for p:

• p/(p - 2) = 8p/(5p - 1)
• 8(p - 2) = 5p - 1
• 8p - 16 = 5p - 1
• 8p - 5p = 16 - 1
• 3p = 15
• p = 5