Question

A line AB passes through the point P(3,-2) with gradient 2, determine the equation of the line CD through P perpendicular to AB.

Answer 1

Answer on Question #82894 – Math – Analytic Geometry

Question

A line AB passes through the point $P(3, -2)$ with gradient 2, determine the equation of the line CD through $P$ perpendicular to AB.

Solution

If gradient (slope) of line AB is $m = 2$, then gradient of the line CD perpendicular to AB is

$$m_1 = -\frac{1}{m} = -\frac{1}{2}$$

So, the equation of the line CD:

$$y = m_1 x + b$$ $$y = -\frac{1}{2} x + b$$

Substitute the coordinates of the point $P$ which lies in the line CD:

$$-2 = -\frac{1}{2} \cdot 3 + b$$ $$b = -\frac{1}{2}$$

Thus, the equation of the line CD is

$$y = -\frac{1}{2} x - \frac{1}{2}$$

Answer: $y = -\frac{1}{2} x - \frac{1}{2}$.

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