Ratio of line segments [Solved!]

X

Given: the coordinates of the endpoints of line segment AC and the fact that a point B lies on the line and AB:BC=1:2.  


We are seeking a method to use to find the coordinates of B.

Relevant page

<a href="http://www.nysedregents.org/geometryre/118/geom12018-exam.pdf">http://www.nysedregents.org/geometryre/118/geom12018-exam.pdf</a>

What I've done so far

I calculated the distance between the endpoints: 15.

I do not know how to use that knowledge to solve for the coordinates of B.

Please help. Thanks.

X

Presumably you are talking about Question 6 on that exam? It's easy enough to answer it just by looking (especially given the MCQ choices)! However, we need to do some calculation, of course.

Your answer for the length is correct. So what will be the distance from A to B?

You could then find the formula for the line AC.

And once you have that distance and the formula, you can use the distance formula to find the point B.

X

The distance, again, is 15.

So the distance between A and B is 5.

Using the distance formula and squaring both sides gives 
`(-5 - x)^2 + (2 - y)^2 = 25`

Not sure if this is the right/best method to find (x,y) other than just looking at the graph.

X

Yeh, as I said, it's pretty easy just to eyeball it.

But if it was a "real" exam (I don't feel MCQ is good for math tests most of the time), you'd need to show working. So let's proceed.

You can also find the equation of the line AC and see where it intersects the circle you found.

There will be 2 intersection, but only one of them helps us in this question. Go for it!

X

Okay the tutorial showed how to partition it.

The distance between the x-coordinates is 9 (since we are going right), between the y-coordinates is -12 (since we are going down).

AB is 1/3 the distance of the total line.

So the x-coordinate of B would be the x-coordinate of A + 1/3 of the run which is 9: -5 + 3 = -2.

Following, the y-coordinate of B would be the y-coordinate of A + 1/3 of the rise which is -12: 2 + (-4) = -2.