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.

Let the point (-4, 2) be F (fountain).  The point (0, 2) will be B (bench) and the point (0, 5) will be S (slide).
A) the distance from F to B would be 4.  We can use the distance formula, but for a horizontal distance such as this it's easier just to count.  The y-coordinates don't change, and the x-coordinates are 4 units apart.
The distance from B to S would be 3.  It is a vertical distance; the x-coordinates don't change, and the y-coordinates are 3 units apart.
B) These 3 points form a right triangle.  The slope from F to B is given by
m=(2-2)/(-4-0)=0/-4=0.  The slope from B to S is given by
m=(5-2)/(0-0)=undefined.  These are negative reciprocals of each other.