# A line segment is bisected by a line with the equation # 3 y - 8 x = 2 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?

The other end is at the point:

When given a the equation of a line in standard form:

All lines perpendicular to the given line will be of the form:

where k is an arbitrary constant.

Write the given equation for the bisecting line in standard form:

Write the equation for all lines perpendicular to equation [3]:

The start of the bisected line segment,

Substitute 1 for x and 3 for y into equation [4] and solve for k:

The equation of the bisected line segment is:

Add 8 times equation [3] to 3 times equation [5]:

The x coordinate of the end can be found by adding the start coordinate to twice the change for the point of intersection:

Substitute

Here is a graph of, the two lines, the start point, and the end point.

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The other end of the line segment is at the point (7, 3).

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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 line segment is bisected by a line with the equation # - 3 y + 2 x = 5 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
- A line segment is bisected by a line with the equation # 6 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?
- A triangle has corners A, B, and C located at #(5 ,2 )#, #(7 ,9 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- How many perpendicular bisectors can be constructed for a line?
- A triangle has corners A, B, and C located at #(3 ,4 )#, #(7 ,5 )#, and #(2 ,9 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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