A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,1 )#, and #(5 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
Now, the distance formula provides the length of altitude CN.
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To find the endpoints and length of the altitude going through corner C of the triangle, follow these steps:

Calculate the slope of the line segment AB using the formula: [ m_{AB} = \frac{y_B  y_A}{x_B  x_A} ]

Use the pointslope form of a line to find the equation of the line perpendicular to AB passing through point C: [ y  y_C = \frac{1}{m_{AB}}(x  x_C) ]

Substitute the coordinates of point C and the slope of AB into the equation to find the equation of the altitude line.

Find the intersection point of the altitude line and the line segment AB by solving the system of equations formed by the altitude line and the line segment AB.

The intersection point gives the endpoints of the altitude.

Calculate the length of the altitude using the distance formula between the intersection point and point C.
By following these steps, you can determine the endpoints and length of the altitude going through corner C of the triangle.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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