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 (−4, 1), Math Middle School is graphed at (1, 1), and Hypotenuse High School is graphed at (−4, −3). 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.

Part B: Find the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work.

Part C: Find the shortest distance, in miles, from Math Middle School to Hypotenuse High School. Show every step of your work.

Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Who went the shortest distance? Explain.

Answer 1

Step-by-step explanation

the answer is D.

Answer 2

a) The shortest distance in miles, from Euclid Elementary School to Math Middle School is: 8 miles

b)The shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School is: 7 miles

c) The shortest distance, in miles, from Math Middle School to Hypotenuse High School is: √113 miles

d) Kaya went the shorter distance

How to solve Euclid Geometry?

a) From the graph, the shortest distance in miles, from Euclid Elementary School to Math Middle School is calculated using euclid distance between coordinates to get:

D = (5 - (-3))

D = 8 miles

b) From the graph, the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School is calculated using euclid distance between coordinates to get:

D = (5 - (-2))

D = 7 miles

c) From the graph, the shortest distance, in miles, from Math Middle School to Hypotenuse High School is gotten using pythagoras theorem as:

D = √(8² + 7²)

D = √113 miles

d) Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle.

Thus:

Deon's distance = 8 + 7 = 15 miles

Kaya traveled from Hypotenuse High to Math Middle along a straight path.

Kya's distance = √113 miles = 10.63 miles

Kaya went the shorter distance