A triangle has corners A, B, and C located at #(8 ,7 )#, #(1 ,5 )#, and #(6 , 3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
The endpts. of Altd. from corner
length of Altd.
Side AB Equation:
Equation for Altd. CD:
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To find the altitude going through corner C of the triangle with vertices A(8, 7), B(1, 5), and C(6, 3), follow these steps:
 Calculate the slope of the line segment AB.
 Use the perpendicular slope relationship to find the slope of the altitude.
 Use the slope of the altitude and the coordinates of point C to write the equation of the altitude in pointslope form.
 Find the intersection point of the altitude with the line containing side AB to determine the endpoints of the altitude.
 Calculate the length of the altitude using the distance formula.
Let's proceed with these steps:

Slope of AB: ( m_{AB} = \frac{y_B  y_A}{x_B  x_A} )

Perpendicular slope relationship: If the slope of a line is ( m ), the slope of any line perpendicular to it is ( \frac{1}{m} ).

Slope of the altitude: Let ( m_{\text{alt}} ) be the slope of the altitude. It will be ( \frac{1}{m_{AB}} ).

Equation of the altitude in pointslope form: Using pointslope form ( y  y_1 = m(x  x_1) ), with ( (x_1, y_1) = (6, 3) ) (coordinates of point C) and ( m = \frac{1}{m_{AB}} ).

Intersection point of the altitude with AB: Solve the equation of the altitude with the equation of line AB to find the intersection point.

Calculate the length of the altitude using the distance formula: ( \text{Length} = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2} ), where ( (x_1, y_1) ) and ( (x_2, y_2) ) are the endpoints of the altitude.
By following these steps, you can find 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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