# 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: