# Question #36cf7

##### 2 Answers

#### Answer:

# b.) : Contd.........

#### Explanation:

**Part a.):** Suppose that, the **required point** (reqd. pt.)

The given pts. are

Recall that,

Knowing that,

#### Answer:

Point P has the coordinates

The points

#### Explanation:

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

So

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.