# A triangle has corners A, B, and C located at #(6 ,8 )#, #(7 ,4 )#, and #(5 ,3 )#, respectively. What are the endpoints and length of the altitude going through corner C?

The coordinates of A, B, and C in triangle ABC are

Let D (h,k) be the perpedicular foot drawn on AB of the given triangle ABC from C (5,3).

Thus, the altitude passing through corner C is CD.

Once more, CD is perpendicular to AB.

contrasting (1) and (2)

entering h's value into (1)

Therefore, the altitude CD endpoint coordinates

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The altitude going through corner C will be perpendicular to the side AB of the triangle. First, calculate the slope of side AB using points A and B. Then, determine the negative reciprocal of this slope to find the slope of the altitude. Using the slope of the altitude and the coordinates of point C, you can find the equation of the line containing the altitude. Finally, find the intersection point of this line with side AB to get the endpoints of the altitude. The length of the altitude can be found using the distance formula between the 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.

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