# A triangle has corners A, B, and C located at #(4 ,7 )#, #(3 ,2 )#, and #(2 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

The coordinates of end point of altitude is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the altitude going through corner C of the triangle with vertices A(4, 7), B(3, 2), and C(2, 1), we first need to determine the equation of the line containing side AB, as it is perpendicular to the altitude we seek. Then, we can find the intersection point of this line with the altitude from point C, which will give us the endpoint of the altitude.

The equation of the line passing through points A(4, 7) and B(3, 2) can be found using the point-slope form: ( y - y_1 = m(x - x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is a point on the line. The slope ( m ) can be found using the formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ) for two points ( (x_1, y_1) ) and ( (x_2, y_2) ).

After finding the equation of the line containing side AB, we can determine its intersection with the altitude from point C. This intersection point will be one endpoint of the altitude. Then, using the distance formula, we can find the length of the altitude from point C to this intersection point.

Here are the steps summarized:

- Find the slope of side AB using points A and B.
- Use the point-slope form to find the equation of the line containing side AB.
- Since the altitude from point C is perpendicular to side AB, its slope will be the negative reciprocal of the slope of side AB.
- Find the equation of the line passing through point C with the slope determined in step 3.
- Solve the system of equations formed by the equations of side AB and the altitude from point C to find the intersection point, which will be an endpoint of the altitude.
- Use the distance formula to find the length of the altitude from point C to the intersection point.

By following these steps, you can determine the endpoints and length of the altitude going through corner C of the triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

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 orthocenter of a triangle with corners at #(2 ,0 )#, #(3 ,4 )#, and (6 ,3 )#?
- What is the orthocenter of a triangle with corners at #(9 , 5 )#, #(3 , 8 )#, and #(5 ,6 )#?
- A triangle has corners A, B, and C located at #(7 ,1 )#, #(4 ,3 )#, and #(5 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- How do you find the equation that is the perpendicular bisector of the line segment with endpoints #(-2, 4)# and #(6, 8)#?
- A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 9 )#, where is the other end?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7