# Thread: find the value of a in coordinate

1. ## find the value of a in coordinate

triangle ABC has its coordinates at A(a, -1) , B(8,-1) , C(5,4). If the base is twice the
height, find a.

can anybody do me a favor on this problem...

thanks a lot

2. ## Re: find the value of a in coordinate

If we assume the base lies along the line $y=-1$, then what is the vertical distance (the altitude of the triangle) from point $C$ to this line?

Once you find the altitude, then what are the $x$-coordinates of the two points on the base line whose distance from point $B$ is twice the altitude?

3. ## Re: find the value of a in coordinate

I suppose the base is intended to be AB, (but it depends on which way you choose to look at it, a badly worded question), so, since A and B have the same y coordinate, the base length will be the difference between their x coordinates.
Also, since A and B have the same y coordinate, it's easy to work out the height of the triangle.
All that's left is to say the base length is double the height and to solve the resulting equation.

4. ## Re: find the value of a in coordinate

Originally Posted by BobP
I suppose the base is intended to be AB, (but it depends on which way you choose to look at it, a badly worded question), so, since A and B have the same y coordinate, the base length will be the difference between their x coordinates.
Also, since A and B have the same y coordinate, it's easy to work out the height of the triangle.
All that's left is to say the base length is double the height and to solve the resulting equation.

According to the book where I got this problem has answer but does not have solution, that is why I'm wondering how this a = -2 from the book.

Hope you understand. Help me understand how to solve in getting a = -2.

Thanks

5. ## Re: find the value of a in coordinate

There is another solution as well, and both are easily found if you follow my suggestion above.