# Triangle Problem: Calculate Perpendicular Bisector

• mr.mair
In summary, a perpendicular bisector is a line that divides a line segment into two equal halves at a 90 degree angle. Its length can be calculated using the Pythagorean theorem and its coordinates can be found using the midpoint formula and the slope of the original line segment. This concept has various real-world applications and a triangle can have up to three perpendicular bisectors, intersecting at the circumcenter of the triangle.
mr.mair
assignment question URGENT!

I having trouble and its urgent some one help
Triangle wit the vertices A(6,-15)B(22,17)and C(24,11)

-midpoint of side A = (14,1)

Question

1.Calculate the equation of the line that is perpindicular bisector of the side triangle.

Use the fact that $$m_{2} = -\frac{1}{m_{1}}$$ for a perpendicular line.

i Still do not get it

Last edited:
but how do i figure out the equation of the line

Bump Bump Bump

The slope of $$AB$$ is $$2$$. So the slope of the perpendicular bisector is $$-\frac{1}{2}$$.

So use the equation $$y-y_{1} = m(x-x_{1})$$.

So $$y - 1 = -\frac{1}{2}( x-14)$$

Last edited:

## 1. What is a perpendicular bisector?

A perpendicular bisector is a line that divides a line segment into two equal halves at a 90 degree angle.

## 2. How do you calculate the length of a perpendicular bisector?

The length of a perpendicular bisector can be calculated by using the Pythagorean theorem, where the length of the bisector is the hypotenuse of a right triangle formed by the original line segment and the bisector.

## 3. How do you find the coordinates of a point on the perpendicular bisector?

To find the coordinates of a point on the perpendicular bisector, you can use the midpoint formula to find the midpoint of the line segment. Then, using the slope of the original line segment, you can find the slope of the perpendicular bisector. Finally, using the coordinates of the midpoint and the slope, you can find the equation of the perpendicular bisector and solve for the desired point.

## 4. How can the perpendicular bisector be used in real-world applications?

The perpendicular bisector has many real-world applications, such as in construction, where it can be used to create right angles and ensure structural stability. It is also used in navigation and surveying to find the midpoint between two points, and in geometry to prove congruence of triangles.

## 5. Can a triangle have more than one perpendicular bisector?

Yes, a triangle can have up to three perpendicular bisectors, each one originating from a different vertex. These bisectors will intersect at a single point, known as the circumcenter of the triangle. This point is equidistant from all three vertices of the triangle.

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