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.
please don't add code stuff to it, that's unnecessary.
To calculate the distances between points on a coordinate plane, we can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Part A: To find the shortest distance from Euclid Elementary to Math Middle School, we can use the formula:
Distance = √[(1 - (-4))^2 + (1 - 1)^2]
= √[5^2 + 0^2]
= √[25 + 0]
= √25
= 5 miles
Part B: To find the shortest distance from Euclid Elementary to Hypotenuse High School, we can use the formula:
Distance = √[(-3 - 1)^2 + (-4 - (-4))^2]
= √[(-4)^2 + (-3 - 1)^2]
= √[16 + (-4)^2]
= √[16 + 16]
= √32
= 4√2 miles (approximately 5.66 miles)
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we can use the formula:
Distance = √[(-3 - 1)^2 + (-4 - 1)^2]
= √[(-4)^2 + (-4)^2]
= √[16 + 16]
= √32
= 4√2 miles (approximately 5.66 miles)
Part D: To determine who went the shortest distance, we compare the distances traveled by Deon and Kaya. Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle, which is a total distance of:
√32 + √25 = 4√2 + 5 ≈ 5.66 + 5 ≈ 10.66 miles
Kaya traveled straight from Hypotenuse High to Math Middle, which is a distance of:
√32 = 4√2 ≈ 5.66 miles
Therefore, Kaya traveled the shortest distance.
why did you type it out all weird I don;t need those check marks there stop being silly
Apologies for the formatting. Here are the answers without the unnecessary additions:
Part A: The shortest distance from Euclid Elementary to Math Middle School is 5 miles.
Part B: The shortest distance from Euclid Elementary to Hypotenuse High School is approximately 5.66 miles.
Part C: The shortest distance from Math Middle School to Hypotenuse High School is approximately 5.66 miles.
Part D: Kaya traveled the shortest distance, approximately 5.66 miles, from Hypotenuse High to Math Middle.