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laiz [17]
3 years ago
12

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

Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0

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

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