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 solve this without adding sqrt? I don't need codes
Part A:
To find the shortest distance from Euclid Elementary School to Math Middle School, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
d = √((1 - (-4))^2 + (1 - 1)^2)
d = √((5)^2 + (0)^2)
d = √(25 + 0)
d = √25
d = 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B:
To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we can again use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
d = √((-4 - (-4))^2 + (-3 - 1)^2)
d = √((0)^2 + (-4)^2)
d = √(0 + 16)
d = √16
d = 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C:
To find the shortest distance from Math Middle School to Hypotenuse High School, we can once again use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates:
d = √((-4 - 1)^2 + (-3 - 1)^2)
d = √((-5)^2 + (-4)^2)
d = √(25 + 16)
d = √41 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is approximately √41 miles.
Part D:
To compare the distances, we need to find the total distances traveled by both Deon and Kaya.
For Deon:
Deon traveled from Hypotenuse High to Euclid Elementary:
Distance = 4 miles
Deon then traveled from Euclid Elementary to Math Middle:
Distance = 5 miles
Total distance traveled by Deon = 4 miles + 5 miles = 9 miles
For Kaya:
Kaya traveled from Hypotenuse High to Math Middle:
Distance = √41 miles (approximately)
Comparing the distances, we see that 9 miles is shorter than √41 miles (approximately).
Therefore, Deon traveled the shortest distance.