# A triangle has corners A, B, and C located at #(2 ,7 )#, #(5 ,3 )#, and #(9 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

endpoints are:

length of

Line AB has two points, and its slope is:

and the following equation would result from using point B in place of point A:

Since height is only one point and its slope is unknown, it is inversely reciprocal of AB's slope because it is perpendicular to AB.

Moreover, the formula

We can use pythagorean formula to get distance between H and C: #CH=sqrt((x_C-x_H)^2+(y_C-y_H)^2) =sqrt((9-5 24/25)^2+(4-1 18/25)^2)=sqrt((3 1/25)^2+(2 7/25)^2) =sqrt((76^2+57^2)/25^2)=sqrt(5776+3249)/25=sqrt(9025)/25=sqrt(25(90*4+1))/25=sqrt(361)/5=19/5#

Or using decimals (calculator may be handy): #CH=sqrt((9-5.96)^2+(4-1.72)^2)=sqrt((3.04)^2+(2.28)^2) =sqrt(9.2416+5.1984)=sqrt(14.44)=3.8#

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The altitude going through corner C has endpoints (9, 4) and the foot of the altitude, which can be found using the equation of the line containing side AB. The length of the altitude can be calculated using the distance formula between these 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.

- What is the centroid of a triangle with corners at #(9 , 2 )#, #(4 , 6 )#, and #(5 , 8 )#?
- If the altitude of an equilateral triangle is #8sqrt3#, what is the perimeter of the triangle?
- What is the orthocenter of a triangle with corners at #(5 ,7 )#, #(2 ,3 )#, and (4 ,5 )#?
- A line segment is bisected by a line with the equation # - 3 y + 5 x = 8 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
- A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?

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