Question

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are

Options

• (3, 2), (2, 4)

• (4, 0), (2, 8)

• (3, 4), (2, 0)

• (4, 3), (2, 4)

Answer 1

(4, 0), (2, 8)

Explanation;

Hint:

x₁ + x₂ = 6 → (1)

y₁ + y₂ = 8 → (2)

x₂ + x₃ = 2 → (3)

y₂ + y₃ = 2 → (4)

x₁ + x₃ = 4 → (5)

y₁ + y₃ = −6 → (6)

Adding (1) + (3) + (5) we get,

2(x₁ + x₂ + x₃) = 3

x₁ + x₂ + x₃ = 6

x₁ + x₃ = 4

∴ x₂ = 6 – 4 = 2

x₂ + x₃ = 2

x₁ = 6 – 2 = 4

Adding (2) + (4) + (6) we get,

2(y₁ + y₂ + y₃) = 4

y₁ + y₂ + y₃ = 2

y₂ + y₃ = 2

∴ y₁ = 2 – 2 = 0

y₁ + y₃ = −6

y₂ = 2 + 6 = 8

∴ The vertices A is (4, 0) and B is (2, 8).