Question

Prove that the line through the point (x₁, y₁) and parallel to the line Ax + By + C = 0 is A (x –x₁) + B (y – y₁) = 0.

Answer 1

Line Ax + By + C = 0

or y = `-"A"/"B" "x" - "C"/"B"`

Slope of line = `-"A"/"B"`

∴ Slope of parallel line = `-"A"/"B"`

The equation of the parallel line passing through (x1, y1)

`"y" - "y"_1 = -"A"/"B"("x" - "x"_1)`

`"B"("y" - "y"_1) = -"A"("x" - "x"_1)`

A(x − x₁) + B(y − y₁) = 0