Q&A for How to Find the Perpendicular Bisector of Two Points

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What if one of the numbers is a negative, and when I try to find the midpoint it gives me 0? The points are A(-4,4) and B(4,8).

Donagan

Top Answerer

Zero is correct. The x-value midway between -4 and +4 is 0. The y-value midway between 8 and 4 is 6. So the midpoint is (0,6).

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Question

What is the exact length of a line joining the points (-12,3) and (8,4)?

Donagan

Top Answerer

Visualize a right triangle, the hypotenuse of which is the line joining the two points. One leg of the triangle has this length: 8 - (-12) = 8 + 12 = 20. The length of the other leg is 4 - 3 = 1. The hypotenuse has this length: √(20² + 1²) = √401. Thus, the distance between the points is 20.025.

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Question

Is a bisector the same as the negative reciprocal of the line?

Donagan

Top Answerer

No. A line's negative reciprocal would be another line perpendicular to it but not necessarily bisecting it.

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Isn't the equation of a line y = mx + c?

Donagan

Top Answerer

Yes, that's the "slope-intercept" form of a straight line's equation. It's usually denoted as y = mx + b, where m is the slope of the line, and b is its y-intercept.

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Question

How can I find the slope of the perpendicular bisected of segment AB?

Community Answer

First, solve the equation segment for AB using the midpoint formula. Then, use the value of the midpoint to find the value of this formula: y-mx+b, but first solve the value slope before applying the y-mx+b formula.

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How do I find the axis of symmetry of a line segment?

Donagan

Top Answerer

An axis of symmetry is the same thing as a perpendicular bisector, so follow the steps in the above article.

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What if the slope is undefined?

Donagan

Top Answerer

A line with an undefined slope is a vertical line (that is, it's parallel to the y-axis).

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Question

How can I find the coordinate of a perpendicular bisector?

Donagan

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A perpendicular bisector is a line. Lines do not have coordinates. Points have coordinates.

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What if, after you have found the mid-point, the slope equals 0?

Donagan

Top Answerer

If the slope is zero, the line is horizontal (parallel to the x-axis), so draw a line through the midpoint parallel to the y-axis, and you have perpendicularly bisected the first line.

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Question

How many bisectors does AB have on a straight line?

Community Answer

Theoretically, an infinite amount, assuming A = (0,0) and B = (1,1) then you can have bisectors that bisect at (0.1,0.1), (0.01,0.01), (0.001,0.001) etc...

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What if the points AB are not defined?

Donagan

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Any undefined points are useless in any graphing application.

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Question

How do I prove that lines are perpendicular?

Community Answer

That's beyond the scope of this Q&A format. See SlideShare.net/1conejo/proving-lines-are-perpendicular.

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Question

Why must we find the reciprocal of the slope?

Donagan

Top Answerer

The negative reciprocal of the slope of line A is the slope of a line perpendicular to line A. You need the slope of the perpendicular line in order to write its equation.

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Question

How to use y=mx+c formula to get a final answer?

Tina X

Community Answer

It depends on your problem. If you are finding the y intercept, you will solve c. If you are to find the slope, you would want to find m.

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Question

What if I have a number where the perpendicular slope is undefined? The points are (-7,3) and (5,3)

Donagan

Top Answerer

That means the two points are on a line parallel to the x-axis. (That line is y=3.) Any line perpendicular to that line would be parallel to the y-axis and have an "undefined" slope (meaning a slope of infinity).

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Is the right bisector the same as the perpendicular bisector?

Donagan

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Yes.

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