I'm having trouble understanding how to get an answer for this problem, I got the answer (I looked in the back of the book for help, hoping It would help me) but I don't know how to get that answer... OH by the way its distance formula... etc..

Problem:
Find all poings having an x-coordinate of 2 whose distance from the point (-2, -1) is 5.

the right answer is:
92, 2); (2, -4)

Let a point have the coordinates (x, y) which you don't know.

However, you know that the x coordinate is 2, hence, the coordinates of the point(s) become (2, y).

Now, the distance formula is:

Distance = \sqrt{(x - x_o)^2 + (y - y_o)^2}

This distance is 5, x = 2, y =? xo = -2, yo = -1. Substitute those into the distance formula:

5 = \sqrt{(2 - (-2))^2 + (y - (-1))^2}

Can you complete it now? Solve for y!

Thanks so much... but I'm still a little bit confused, every time I try to solve it I end up with a weird answer.. .

Would you be so kind as to show what you did? We can help you stop your mistakes so that you know where to be more careful next time :)

I finally figured out half of it I think. Here's what I put:

5 =sqrt(2-(-2))^2+(y-(-1))^2)
5 =sqrt(4)^2+(y+1)^2
5 =sqrt(16+y^2+2y+1)
5 =sqrt(17+y^2+2y)
25 =17+y^2+2y -------- (I squared both sides to cancel out the sqrt)
8 =y^2+2y
4y =y^2
y=2
(2,2)
that's how I figured it... Please correct my mistakes if you can

Those are good procedures up to this line:

8 =y^2+2y

This is a quadratic equation, and so, it cannot become

4y =y^2

This, instead becomes:

0 =y^2+2y - 8

Then, factorise:

0 =(y - 2)(y +4)

This done, you get:

y - 2 = 0 or y + 4 = 0

This gives you two answers, which are what the given answers say (You already know the x coordinate, which is x = 2) :)

OH! Ok! Thank you SO much... I completely understand now... thanks again!

You're welcome :)