# Find the coordinates for a point in a triangel

#### Sara33

##### New member
A triangel in a coordinate system is given by the points A (-1, 4), B (8,1) and C (4, 9). A height is drawn against the side AB. Calculate the coordinates for the point where the height meets the side AB.

First I calculated the slope of the line which goes from point A to B. This is -1/3. The line which goes from C against the side AB is has to be perpendicular against A and B. This means it has a slope which is 3.

y2-y1/x2-x1=slope
9-y1/4-x1= 3
From here I do not know how to continue. Can you please help me? Thank you in advance.

#### wjm11

##### Senior Member
A triangel in a coordinate system is given by the points A (-1, 4), B (8,1) and C (4, 9). A height is drawn against the side AB. Calculate the coordinates for the point where the height meets the side AB.

First I calculated the slope of the line which goes from point A to B. This is -1/3. The line which goes from C against the side AB is has to be perpendicular against A and B. This means it has a slope which is 3.
y2-y1/x2-x1=slope
9-y1/4-x1= 3
From here I do not know how to continue.

Good work. You’re almost there.

You now have a slope, 3, and a point, C(4,9); just use that info to write the equation for your line. With the information you have, I would suggest point-slope form:

y – y1 = m(x – x1), where m is the slope and (x1,y1) is a point you know. For example, if slope is 5 and the point is (3,1), then the line equation is

y – 1 = 5(x – 3)

#### Subhotosh Khan

##### Super Moderator
Staff member
Sara33 said:
A triangel in a coordinate system is given by the points A (-1, 4), B (8,1) and C (4, 9). A height is drawn against the side AB. Calculate the coordinates for the point where the height meets the side AB.

First I calculated the slope of the line which goes from point A to B. This is -1/3. The line which goes from C against the side AB is has to be perpendicular against A and B. This means it has a slope which is 3.

y2-y1/x2-x1=slope
9-y1/4-x1= 3
From here I do not know how to continue. Can you please help me? Thank you in advance.
Let the point of intersection be D.

You have calculated that the slope of CD is 3. CD passes through (4,9).

Equation of aline passing through (x[sub:3tt0qhjj]1[/sub:3tt0qhjj],y[sub:3tt0qhjj]1[/sub:3tt0qhjj]) with a slope 'm' is:

(y - y[sub:3tt0qhjj]1[/sub:3tt0qhjj]) = m * (x - x[sub:3tt0qhjj]1[/sub:3tt0qhjj]) ? (y - 9) = 3 * (x - 4) .......................(1)
Now you know equation of line CD.

Equation of line AB would be:

(y - 4) = (-1/3) * (x + 1) .........................................................................(2)

Now solve for the common point in line CD and AB.

#### Sara33

##### New member
Thank you very much! I understand the explaination.

#### Denis

##### Senior Member
Sara, if you didn't already do it, I suggest you graph the 3 given points (takes less than a minute!),
draw the triangle, draw the perpendicular CD (C to line AB), and you will "see" that the coordinates
of D are (2,3); doing this helps in determining if you're on the right path...

#### Sara33

##### New member
Ok thank you Denis, it was a good advice. I will use it next time a similar problem occurs.