A triangle has corners A, B, and C located at #(1 ,8 )#, #(2 ,3 )#, and #(5 ,9 )#, respectively. What are the endpoints and length of the altitude going through corner C?
Now, the length of altitude CN is given by distance formula
hence, the end points of altitudes are
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To find the altitude going through corner C of the triangle, follow these steps:
- Calculate the slope of the line passing through points A and B. Let's call this slope ( m_{AB} ).
- The perpendicular slope to ( m_{AB} ) is the negative reciprocal of ( m_{AB} ), denoted as ( -\frac{1}{m_{AB}} ). Let's call this ( m_{\perp} ).
- Using point C and the slope ( m_{\perp} ), find the equation of the line passing through C that is perpendicular to AB.
- Find the intersection point of this perpendicular line and the line containing AB. This point will be the foot of the altitude, let's call it D.
- The distance from point C to point D is the length of the altitude.
Once you find the endpoint D, you will have the altitude and its length.
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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.
- What is the centroid of a triangle with corners at #(1, 1 )#, #(3, 2 )#, and #(8 , 6 )#?
- In triangle ABC, AD and BE are altitudes and AP and BQ are angle bisectors at A and B respectively, where P lies on CD and Q lies on CE. If #angle# PAD = 6° and #angle#QBE =18° , what is the degree of #angle#BCA?
- A triangle has corners at #(6 , 1 )#, ( 4, 2 )#, and #( 2, 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
- A line segment is bisected by a line with the equation # - 5 y + 3 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?
- What is the orthocenter of a triangle with corners at #(1 ,1 )#, #(6 ,6 )#, and (4 ,6 )#?

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