# Thread: Anayltic geometry

1. ## Anayltic geometry

Question:
The line segment joining A(1,3) and B(-2,-1) is extended through each end by a distance equal to it's original length.Find the co-ordinates of the new endpoint.

Attempt
I don't know what to do.

2. Hello,
Originally Posted by mj.alawami
Question:
The line segment joining A(1,3) and B(-2,-1) is extended through each end by a distance equal to it's original length.Find the co-ordinates of the new endpoint.

Attempt
I don't know what to do.
Work in terms of vectors.

The coordinates of a vector is the difference of each coordinate of its endpoints :
$\vec{AB} ~:~ (x_B-x_A ~,~y_B-y_A)=(-3,-4)$

And $\vec{CA}=\vec{AB}=\vec{BD}$

That should be enough ^^

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
seeing your other thread, you can also work with midpoints.

A is the midpoint of CB. Find the coordinates of C.
B is the midpoint of BD. Find the coordinates of D.

(draw a sketch if you can't see what I'm talking about )