Question

A map of three public schools was created using a coordinate plane where the origin represents the center of the town. Euclid Elementary School is graphed at (−3, 5), Math Middle School is graphed at (5, 5), and Hypotenuse High School is graphed at (−3, −2). Each unit on the graph represents 1 mile. Part A: Find the shortest distance, in miles, from Euclid Elementary School to Math Middle School. Show every step of your work. (2 points) Part B: Find the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work. (2 points) Part C: Find the shortest distance, in miles, from Math Middle School to Hypotenuse High School. Show every step of your work. (4 points) Part D: Javi traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Braylen traveled from Hypotenuse High to Math Middle along a straight path. Who went the shortest distance? Explain. (4 points)

Answer 1

A: The shortest distance from Euclid Elementary School to Math Middle School is 8 miles.

B: The shortest distance from Euclid Elementary School to Hypotenuse High School is 7 miles.

C: The shortest distance from Math Middle School to Hypotenuse High is 10.63 miles.

D: Braylen went the shortest distance.

Part A.

In order to determine the shortest distance from Euclid Elementary School to Math Middle School, we would use the side lengths of the right-angled triangle formed by points;

Shortest distance = 5 - (-3)

Shortest distance = 5 + 3

Shortest distance = 8 miles.

Part B.

For the shortest distance from Euclid Elementary School to Hypotenuse High School, we have the following;

Shortest distance = 5 - (-2)

Shortest distance = 5 + 2

Shortest distance = 7 miles.

Part C.

In order to determine the shortest distance from Math Middle School to Hypotenuse High, we would apply Pythagorean's theorem by calculating the length of the hypotenuse of the right-angled triangle;

`z^2=x^2 + y^2 \\\\z^2=8^2 + 7^2 \\\\z^2=64+49\\\\z=√(113)`

z = 10.63 miles.

Part D.

The distance traveled by Javi can be calculated as follows;

Distance = 8 + 7

Distance = 15 miles.

The distance traveled by Braylen can be calculated as follows;

Distance = 10.63 miles.

Therefore, Braylen went the shortest distance.