Question

Write an Equation of the perpendicular bisector of the segment with endpoints Q(-2,0) and R(6,12).

Answer 1

The equation of perpendicular bisector of QR is:

$y = -\frac{2}{3}x+\frac{22}{3}$

Step-by-step explanation:

Given points are:

$Q(-2,0)\ and\ R(6,12)$

First of all, we have to find the slope of the given line

So,

$m = \frac{y_2-y_1}{x_2-x_1}$

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

$m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}$

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}$

The bisector will pass through the mid-point of QR

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)$

Slope-intercept form of equation is:

$y = m_2x+b$

Putting the value of slope

$y = -\frac{2}{3}x+b$

Putting (2,6) in the equation

$6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}$

So,

$y = -\frac{2}{3}x+\frac{22}{3}$

Hence,

The equation of perpendicular bisector of QR is:

$y = -\frac{2}{3}x+\frac{22}{3}$

Keywords: Mid-point, equation of line

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