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

##### 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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