# b.) : Contd.........
Part a.): Suppose that, the required point (reqd. pt.)
The given pts. are
Point P has the coordinates
For any of these it makes sense to draw a diagram if you can. I haven't here, but you should. Do as I say, not as I do. ;-)
For part (a), we can treat each direction separately. We want the sum in
I've just subtracted each of the
Same method for
For part (b) we have the coordinates of two points on a triangle,
Draw a diagram!
To make the triangle scalene, we would need two of its sides to be the same length. To make it equilateral, all three sides would need to be the same length.
Let's calculate the length of the side we already know:
We need to choose values of
Try first for
Now, in the real numbers, we cannot do this (in imaginary numbers we can, but you're probably not studying that at the moment).
Since we can't find a value that makes this side have a length of
Let's try for
(I'm gonna go around this a long way to make sure it's clear:
I would use the quadratic formula to solve this quadratic: use your favourite method.
So there are two solutions - two points on the
Test this on your diagram.