Question

An equation of the perpendicular bisector of the line segment with end points (3,0) and (-3,0) is

Answer 1

Answer:

$x = 0$

Step-by-step explanation:

Given

$(x_1,y_1) = (3,0)$

$(x_2,y_2) = (-3,0)$

Required

The equation of the perpendicular bisector.

First, calculate the midpoint of the given endpoints

$(x,y) = 0.5(x_1 + x_2, y_1 + y_2)$

$(x,y) = 0.5(3-3, 0+ 0)$

$(x,y) = 0.5(0, 0)$

Open bracket

$(x,y) = (0.5*0, 0.5*0)$

$(x,y) = (0, 0)$

Next, determine the slope of the given endpoints.

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

$m = \frac{0 - 0}{-3- 3}$

$m = \frac{0}{-6}$

$m = 0$

Next, calculate the slope of the perpendicular bisector.

When two lines are perpendicular, the relationship between them is:

$m_2 = -\frac{1}{m_1}$

In this case:

$m = m_1 = 0$

So:

$m_2 = -\frac{1}{0}$

$m_2 = unde\ fined$

Since the slope is $unde\ fined$, the equation is:

$x = a$

Where:

$(x,y) = (a,b)$

Recall that:

$(x,y) = (0, 0)$

So:

$a = 0$

Hence, the equation is:

$x = 0$