Question

Given the three points, A(2,1), B(-3,6), and C(5,-1)
e) find the altitude to the side AC

HOW? :(

Answer 1

First find the slope of AC using slope = \(\large \frac{y_2-y_1}{x_2-x_1}\).
Since the slope of the altitude is perpendicular to AC, the slope is its negative reciprocal, or
Slope of altitude, m =\(\large -\frac{x_2-x_1}{y_2-y_1}\).
For this line to pass through point A, then the point-slope form of a line can be used:
\((y-y_1=m(x-x_1)\)
where (x1,y1) are the coordinates of point A.

Answer 2

can u show me the illustration? :(
by the way thanks in the way of solution

Answer 3

@mathmate so the answer is an equation ?

Answer 4

Another method:
Distance of the point (p, q) from the line \(\Large Ax + By + C = 0 \) is:
\(\Large \frac{Ap + Bq + C}{\sqrt{A^2 + B^2}} \)

If you can find the equation of the line AC, you can plug the numbers in the above formula and find the distance of point B from the line AC.

Answer 5

@aum so that the formula above is for looking the distance by using the coefficients of the find equation

Answer 6

Correct. This is just another way to solve the same problem:
http://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line

Answer 7

hmm. in my given problem I think it's just looking for the equation because we are in that topic yesterday in school
at ur formula it will be our next topic thanks again! :)

Answer 8

It says: "find the altitude to the side AC"

I think it is asking for the length of the altitude and hence I suggested the above formula. But if it asking for the equation it should have said find the equation to the altitude line.

Answer 9

i also confused in the question :(

Answer 10

Does the answer have a number or an equation?

Answer 11

what?

Answer 12

Does the answer to this question in your book have just a number or does it have an equation?

Answer 13

it was been dictated by my prof

Answer 14

Okay, you don't have the answer yet. Find out from your professor whether you need to find the length of the altitude or the equation of the altitude.
If I were you, I'd find both in separate papers and submit the right one after talking to your professor.

Answer 15

yup thanks!

Answer 16

Yes, @aum. I misread the question.
The answer should be a distance, and the distance formula you proposed should do the job, as long as the equation to the line AC has been found.
Thank you for your valuable help!

The triangle does look weird (too flat).
As aum mentioned, steps are:
1. find the equation of line AC using slope between A and C, and the point slope formula for a line passing through A or through C (in fact, both). Convert equation to general form :
Ax+By+C=0.
2. Use the altitude formula given bu aum to find the length of the altitude.
@mz_samosino