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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 :

Mhanifago

Answer:

  • C = (6, 7)

Step-by-step 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)

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