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# coordinate question

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What is the intersection point of the line y = -2x + 5 and the line perpendicular to it that passes through the point (5,5)?

Jan 19, 2021

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Perpendicular: Product of slopes = -1.

Let m be the slope of the line perpendicular to y = -2x + 5.

Slope of y = -2x + 5 is -2.

This means $$-2\cdot m = -1$$, i.e., $$m = \dfrac12$$.

The required line passes through (5, 5) and the slope is 1/2. We use the point-slope form of the equation of a straight line.

The equation of the required line is

$$y - 5 = \dfrac12 \left(x - 5\right)\\ 2y - 10 = x - 5\\ \boxed{x - 2y + 5 = 0}$$

Jan 19, 2021