# How do you find the perpendicular bisector of a line segment?

The line through the interception points of the circles with centers in each end point of the segment and the segment as radius

The bisector is the line trough the interception points of the circles witn centers in each end point of the segment and the segment as radious

Both interception points are at equal distance of each end point of the segment and so, at half distance of each one.

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To find the perpendicular bisector of a line segment, follow these steps:

- Determine the midpoint of the line segment by averaging the coordinates of its endpoints.
- Find the slope of the line segment using the formula: ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ), where ( (x_1, y_1) ) and ( (x_2, y_2) ) are the coordinates of the endpoints.
- Calculate the negative reciprocal of the slope found in step 2 to find the slope of the perpendicular bisector.
- Use the point-slope form of a line, ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is the midpoint found in step 1 and ( m ) is the slope of the perpendicular bisector from step 3, to write the equation of the perpendicular bisector.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners A, B, and C located at #(4 ,5 )#, #(3 ,6 )#, and #(8 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(7 ,6 )#, #(9 ,3 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- Let A be #(−3,5)# and B be #(5,−10))#. Find: (1) the length of segment #bar(AB)# (2) the midpoint #P# of #bar(AB)# (3) the point #Q# which splits #bar(AB)# in the ratio #2:5#?
- A line segment is bisected by a line with the equation # 9 y - 2 x = 5 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?
- What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,7 )#?

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