# A triangle has corners A, B, and C located at #(2 ,7 )#, #(5 ,3 )#, and #(2 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

The end points of the altitude are

The length is

Determine the line segment AB's equation and slope.

To determine the equation of the line segment AB, use one of the points and the slope:

To calculate the slope of the altitude, use the slope of AB.

To determine the altitude equation, use point C and the slope:

To determine the x coordinate of the point of intersection, use equations [1] and [2]:

To find the y coordinate, use any equation (I'll use [2]):

The separation between the two points is the altitude's length:

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The endpoints of the altitude going through corner C are (2, 4) and the intersection point of the line passing through points A and B with the line perpendicular to it passing through point C. The length of the altitude can be calculated using the distance formula between the two endpoints.

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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 #(3 ,4 )#, #(2 ,5 )#, and #(2 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
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- What is the orthocenter of a triangle with corners at #(1 ,2 )#, #(5 ,6 )#, and (4 ,6 )#?
- A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
- Given 2 numbers #(a,b)# it is possible to perform geometrically the following algebraic operations: a+b, a−b, a*b, a/b. Use only a straight edge and compass to show each operation?

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