Question

I WILL GIVE BRAINLIEST IF ANSWERED CORRECTLY

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

Part A: The shortest distance between Euclid Elementary School and Math Middle School in miles is 8 miles.

Part B: The shortest distance between Euclid Elementary School and Hypotenuse High School in miles is 7 miles.

Part C: The shortest distance between Math Middle School and Hypotenuse High School in miles is 10.6 miles.

Part D: Braylen took the shortest route.

What is the distance between two points?

Assume we have two points with coordinates and. The following rule determines the shortest distance between them:

D=√(x₂-x₁)²+(y₂-y₁)²

The Pythagorean Theorem is used to obtain this formula, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

The coordinates for item an are as follows:

Euclid: (-3, 5).

Math: (5,5).

D=√(5+3)²+(5-5)²

D=8

Each unit is one mile, for a total of eight miles.

The coordinates for item b are as follows:

Euclid: (-3, 5).

Hypotenuse: (-3, -2).

D=√(-3+3)²+(-2-5)²

Hence 7 miles.

The coordinates for item c are as follows:

Math: (5, 5).

Hypotenuse: (-3, -2).

D=√(-3-5)²+(-2-5)²

D=√113

Hence 10.6 miles.

The coordinates for item D are as follows:

Javi: 8+ 7 = 15 miles.

Braylen: 10.6 miles.

10.6 < 15,

Hence Braylen went the shortest distance.

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