# Thread: coordinate geometry

1. ## coordinate geometry

The vertices of the triangle ABC have coordinates A(-5,3) , B(-2,0) and
C(4,-1) . Find the equations of the sides of the triangle.

2. The equation of line joining two points
(a,b) and (c,d) is given by

$\displaystyle (y -b) = \frac{(d-b)}{(c-a)} \times{(x-a)}$

You have three points and you are asked to find the equations of those three lines which join them
Now think ahead yourself and tell if you feel trouble

3. Originally Posted by ADARSH
The equation of line joining two points
(a,b) and (c,d) is given by

$\displaystyle (y -b) = \frac{(d-b)}{(c-a)} \times{(x-a)}$

You have three points and you are asked to find the equations of those three lines which join them
Now think ahead yourself and tell if you feel trouble

I have not come across this equation, my book tells me to use this equation.

$\displaystyle \frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}$ but I have got three points, so am not sure how to work it out.

4. Originally Posted by Tweety
I have not come across this equation, my book tells me to use this equation.

$\displaystyle \frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}$ but I have got three points, so am not sure how to work it out.
The equation is the same, if you set $\displaystyle (a,\;b)=(x_1,\;y_1)$, $\displaystyle (c,\;d)=(x_2,\;y_2)$, and divide by $\displaystyle y_2 - y_1$.

You have three lines, so you will need to apply the equation three times. Just substitute the coordinates for each pair of points.

5. Make a sketch on the coordinate plane will make things easier .

Let me start you off with the line AB .

The gradient is -1 and we know the line passes through point (-5,3) or
(-2,0)

y-y1=m(x-x1)
thus , y=-x-2

do it this way for the remaining two sides of the triangle .