A triangle has corners A, B, and C located at #(1 ,7 )#, #(7 ,4 )#, and #(2 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
1 Answer
The end points are (2, 8) and (4.6, 5.2), The length is
Explanation:
Going from point A to B we go right 6 and down 3, therefore, the slope is
The equation of the line through points A and B is:
The altitude through point C will perpendicular to the above line, thereby, making its slope the negative reciprocal of
The equation of the line through point C is:
Set the right sides of the two equations equal and then solve for the x coordinate of their intersection:
The length, a, of the altitude is: