Question

A swimming pool is represented on a coordinate grid with the following vertices: Vertex A is at (−2,−3) . Vertex B is at ​​ (−2,5) . Vertex C is at (3,5) . Vertex D is at (3,−3) . While Jared cleans the pool, he walks from vertex A to vertex B, then to vertex C, then to vertex D, and then back to vertex A. One unit on the grid equals 1 yard. What is the total distance Jared has walked? Enter your answer in the box.

Answer 1

Answer:

26 yards.

Step-by-step explanation:

We can find the distance walked by Jared by finding the distances between each of the given vertex of swimming pool. We will use distance formula to find the distances between each vertex.  

$\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2--2)^{2}+(-3-5)^{2}}$  

$\text{Distance between vertex A and vertex B}=\sqrt{(-2+2)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(0)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{64}=8$

Now let us find distance between vertex B and vertex C.

$\text{Distance between vertex B and vertex C}=\sqrt{(-2-3)^{2}+(5-5)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{(-5)^{2}+(0)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{25}=5$

Now let us find distance between vertex C and vertex D.

$\text{Distance between vertex C and vertex D}=\sqrt{(3-3)^{2}+(5--3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{(0)^{2}+(5+3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{64}=8$

Now let us find distance between vertex D and vertex A.

$\text{Distance between vertex D and vertex A}=\sqrt{(3--2)^{2}+(-3--3)^{2}}$  

$\text{Distance between vertex D and vertex A}=\sqrt{(3+2)^{2}+(-3+3)^{2}}$    

$\text{Distance between vertex D and vertex A}=\sqrt{(5)^{2}+(0)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{25}=5$

Now let us add all these distances to find the total distance walked by Jared.  

$\text{Total distance walked by Jared}=8+5+8+5$

$\text{Total distance walked by Jared}=26$  

Since we have been given that one unit on the grid equals 1 yard,   therefore, Jared walked a distance equal to 26 yards.