Question

Prove that If the points (x₁, y₁), (x₂, y₂), (x₃, y₃) are on a single line, then the points (3x₁ + 2y₁, 3x₁ – 1y₁), (3x₂ + 2y₂, 3x₂ – 2y₂), (3x₃ + 2y₃, 3x₃ – 2y₃) are also on a single line. Would this be true if we take some other numbers instead of 3 and 2?

Answer 1

(x₁,y₁), (x₂,y₂), (x₃,y₃) are in the same line

Then, \(\frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_1}{x_3-x_1}\)

∴ They are in the same line

Yes it is possible.