geometry
posted by sequoia .
find the distance points of each pair of points 12.G(0,0),H(3,4) 13.N(5,2),K(2,8) 14.A(4,4),W(2,2)

I'll do #12. You should be able to follow the method for 13,14.
You calculate the distance between two points by making the line joining them the hypotenuse of a right triangle with horizontal and vertical legs.
In this case, G=(0,0) and H=(3,4). So, to get the triangle, note that the point P=(3,0) has as its base the line GP and its height is PH. You could also use the point Q=(0,4), in which case the base would be above the hypotenuse.
In either case, you can now easily see that the legs have length 3 and 4. So, the hypotenuse has length sqrt(3^2 + 4^2) = sqrt(25) = 5.