Question

if P(9a-2, -b) divides the line segment joining A(3a+1, -3) and B (8a, 5) in the ratio 3:1. find the values of a and b.

Answer 1

To find the values of a and b we need to use the sectional formula, which is m₁x₂ + m₂x₁ / m₁+m₂ , m₁y₂ + m₂y₁ / m₁+m₂

P(x) = m₁x₂ + m₂x₁ / m₁+m₂
⇒ 9a-2 = 3(8a) + 1(3a+1)
⇒ 4(9a-2) = 24a +3a+1
⇒ 36a-8 = 27a +1
⇒ 9a = 9
⇒ a=1
∴ The value of a is 1

P(y) = m₁y₂ + m₂y₁ / m₁+m₂
⇒ -b = 3(5) + 1(-3) / 3+1
⇒ -b = 15 -3 /4
⇒ -b = 12/4
⇒ -b = 3
⇒ b = -3
∴The value of b = -3

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Answer 2

Answer:

a= 1 and b= -3

Step-by-step explanation:

Hope it helps you