Acoordinate grid is used to make a map of the park. the location of the drinking fountain is (-4, 2) the location of the bench is (0,2) and the location of the center of the slide is (0, 5).

(a)what is the distance from the drinking fountain to the bench? what is the distance from the bench to the center of the slide? explain your reasoning.

(b)what type of triangle is created by the three locations? explain.

plz hurry and answer plz! : )

Please see attached file

P.S. I noticed I did the entire problem wrong so I had to go back and re-do the entire thing.

Here we have the following points: (-4, 2), (0, 2), and (0, 5), point 1, point 2, point 3 respectively. In question 1, we are to the find the distance from point 1 to point 2, and point 2 to point 3.

A coordinate on the coordinate-plane(graph) is known as (x, y), where in this case we can separate the points:
x= -4, 0, 0
Y = 2, 2, 5
respectively.

The distance from point 1 to point 2 is on the same axis, the x-axis. Thus, we only need to take the distance from -4 to 0.Distance, in its definition, cannot be negative. Of course we still can’t go back in time to go negative distances, that’s why. As of yet.

So we take the absolute value: |-4+0| = 4 even though you can also do |-4-0| = 4 since one of the numbers is at 0.

Now, the distance from point 2 to point 3 is on the same axis, the y-axis. Thus we only need to take the distance from 2 to 5.

5 is bigger than 2, and also on the graph, higher than 2, so the distance would be |5-2| = 3.

Distance, respectively to your question, is 4 and 3.

For question 2, we get a triangle. Specifically, the right triangle. I have this highlighted out(you may have to look a little closely) but if you connect the very remaining two points (point 1 to point 3) without a side and make a line segment between the two points, you get a right triangle.

A right triangle must have a 90 degree angle. A 90 degree angle is formed by two perpendicular lines/rays/etc. The x-axis and y-axis, the two big fat lines going up and down(y-axis) and left and right(x-axis) are perpendicular to each other. That’s how we get the only 90 degree angle.

For a little extra I’ll prove by using Pythagorean Theorem too(don’t include this in your answer).

a^2+b^2=c^2 where c is the hypotenuse and a and b are legs of the triangle.

4^2+7^2=c^2
16+49=c^2
65=c^2
c=√65

Of course if you go on google and search up the distance from point 1 to point 3, it is √65.

So there you go!
:)

P.P.S. If you don't know what absolute value is, it means that the number or answer to the equation inside of it will always turn positive. It doesn't matter if the number is negative or positive already.

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4