A triangle has corners A, B, and C located at #(8 ,3 )#, #(4 ,5 )#, and #(6 , 7 )#, respectively. What are the endpoints and length of the altitude going through corner C?
Endpoints of Altitude: Length of Altitude:
Given: First let's consider the line through Looking at the altitude from Finding the point of intersection of the altitude with the base
Calculating the length of the Altitude
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To find the altitude going through corner C of the triangle, follow these steps:
- Calculate the slope of the line containing side AB, which passes through corners A and B.
- Determine the negative reciprocal of the slope of side AB to find the slope of the altitude passing through corner C.
- Use the point-slope form to write the equation of the altitude passing through corner C using the coordinates of corner C and the slope of the altitude.
- Find the intersection point of this altitude with the line containing side AB to determine the endpoints of the altitude.
- Calculate the distance between the intersection point and corner C to find the length of the altitude.
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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.
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.
- A triangle has corners A, B, and C located at #(5 ,2 )#, #(2 ,5 )#, and #(8 ,7 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(2 ,4 )#, and (8 ,6 )#?
- What is the orthocenter of a triangle with corners at #(3 ,3 )#, #(2 ,4 )#, and (7 ,9 )#?
- A line segment is bisected by a line with the equation # 3 y - 8 x = 2 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
- A triangle has corners A, B, and C located at #(5 ,5 )#, #(3 ,9 )#, and #(4 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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