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.

Asked by Abhisek | 1 year ago |  107

1 Answer

Solution :-

Let the slope of line Ax + By + C = 0 be m

Ax + By + C = 0

So, y = \( -\dfrac{A}{B}x+\dfrac{C}{B}\)

m = \( -\dfrac{A}{B}\)

By using the formula,

Equation of the line passing through point (x1, y1) and having slope 

m = \( -\dfrac{A}{B}\) is

y – y1 = m (x – x1)

y – y1\( -\dfrac{A}{B}\) (x – x1)

B (y – y1) = -A (x – x1)

A(x – x1) + B(y – y1) = 0

So, the line through point (x1, y1) and parallel to the line 

Ax + By + C = 0 is A (x – x1) + B (y – y1) = 0

Hence proved.

Answered by Pragya Singh | 1 year ago

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