A coordinate grid is used to make a map for the park. The location of the drinking fountain is (7, 3); the location of the bench is (2, 3); and the location of the center of the slide is (7, -5). Plot these points
(a) What is the distance from the center of the slide to the drinking fountain?

(b) What is the distance from the drinking fountain to the bench? Explain you reasoning.

(c) What type of triangle is created by the three locations? Explain.

(a) There is a distance of 8 units from the center of the slide to the fountain.

(b) There is a distance of 5 units between the fountain and the bench.

(c) A right-angled scalene triangle is formed by the three points.

Step-by-step explanation:

Step 1:

First, we plot the points of the three locations. The drinking fountain at (7, 3), the bench at (2, 3) and center of the slide at (7, -5).

To calculate the distance between two points on a graph we use the formula; .

Step 2:

The center of the slide is at (7, -5) so ( , ) is (7, -5) and the fountain is at (7, 3) so (, ) = (7, 3).

So distance is = √ = 8 units.

Step 3:

The fountain is at (7, 3) so ( , ) is (7, 3) and the bench is at (2, 3) so (, ) = (2, 3).

So distance is = √ = 5 units.

Step 3:

By plotting the points on the graph, we get a horizontal line connecting the bench and the fountain and a vertical line by connecting the fountain and the slide.

So it is a right-angled triangle and since the line joining the bench and the slide is the hypotenuse, it will be longer than the other sides.

So the right-angled triangle is also scalene.