# A triangle has corners A, B, and C located at #(8 ,3 )#, #(4 ,5 )#, and #(2 , 7 )#, respectively. What are the endpoints and length of the altitude going through corner C?

End points of the altitude are

Length of altitude

As shown in the diagram,

The slope of

The equation of

The equation of

Solving (1) and (2) we get :

So endpoints of altitude

Length of altitude

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The endpoints of the altitude going through corner C are the coordinates of C and the foot of the altitude, which we'll denote as D. To find the foot of the altitude, we can use the formula for the altitude of a triangle from a given vertex:

( x_D = \frac{{x_A + x_B + x_C}}{3} ) and ( y_D = \frac{{y_A + y_B + y_C}}{3} )

Once we have the coordinates of D, we can calculate the length of CD using the distance formula:

( CD = \sqrt{{(x_C - x_D)^2 + (y_C - y_D)^2}} )

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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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