Question

A line segment AB is increased along its length by 25% by producing it to C on the side of B . If A and B have the coordinates ( 1 , 2 ) and ( 5 , 6 ) respectively then find the coordinates of C.

Ans : ( 6 , 7 )

*Please show your workings* ​

Answer 1

• C = (6, 7)

Explanation:

Coordinates of point B in terms of A and C:

• x = x₁ + (x₂ - x₁)*a/(a + b)
• y = y₁ + (y₂ - y₁)*a/(a + b)
• B(x, y) = (5, 6), A(x₁, y₁) = (1, 2), C(x₂, y₂) = ?

Find the coordinates:

• 5 = 1 + (x₂ - 1)*4/5 ⇒ 4 = 4/5*(x₂ - 1) ⇒ x₂ - 1 = 5 ⇒ x₂ = 6
• 6 = 2 + (y₂ - 2)*4/5 ⇒ 4 = 4/5(y₂ - 2) ⇒ y₂ - 2 = 5 ⇒ y₂ = 7

• C = (6, 7)