# A triangle has corners A, B, and C located at #(3 ,8 )#, #(7 ,5 )#, and #(2 ,9 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Coordinates of CF (2,9) , (47/25, 221/25))

Length of Altitude CF =

length of the CF altitude

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The altitude going through corner C of the triangle with vertices at (3, 8), (7, 5), and (2, 9) has endpoints at (2, 9) and the foot of the altitude, which we'll denote as point D. To find the foot of the altitude, we need to find the intersection point of the line passing through A and B (the base of the triangle) and the perpendicular line passing through C.

- Find the slope of line AB using the coordinates of points A and B.
- Find the negative reciprocal of the slope of AB to get the slope of the line perpendicular to AB passing through point C.
- Use the slope of the perpendicular line and the coordinates of point C to find the equation of the perpendicular line.
- Find the intersection point of the perpendicular line and the line AB to get the coordinates of point D.

Once you have the coordinates of point D, you'll have the endpoints of the altitude. Then, you can calculate the length of the altitude using the distance formula between points C and D.

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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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- A triangle has corners A, B, and C located at #(2 ,2 )#, #(3 ,4 )#, and #(6 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- Let #P(x_1, y_1)# be a point and let #l# be the line with equation #ax+ by +c =0#. Show the distance #d# from #P->l# is given by: #d =(ax_1+ by_1 + c)/sqrt( a^2 +b^2)#? Find the distance #d# of the point P(6,7) from the line l with equation 3x +4y =11?
- A line segment is bisected by a line with the equation # -3 y + 7 x = 1 #. If one end of the line segment is at #(9 ,2 )#, where is the other end?

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