A triangle has corners A, B, and C located at #(5 ,2 )#, #(7 ,9 )#, and #(9 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
1 Answer
The endpoints are
The distance is
Explanation:
Use the point-slope form of the equation of a line to write the equation of the line through points A and B:
We need the above form and the standard form:
The slope of the altitude through point is the negative reciprocal of the slope in equation [1],
Use the point-slope form of the equation of a line to find the equation of the altitude through point C:
To find the x coordinate of the other endpoint, subtract equation 3 from equation [1]
To find the y coordinate of the other endpoint, substitute the above into equation [3]:
Use equation [2] to find the length of the altitude: