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.
Also, could you not add sqrt and d? I don't need you to make an actual formula I just need answers, and show your work, please.
Part A: To find the shortest distance between Euclid Elementary School and Math Middle School, we can use the distance formula.
The distance formula is given by: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the coordinates of Euclid Elementary School (x1, y1) = (-4, 1) and Math Middle School (x2, y2) = (1, 1) into the formula:
distance = sqrt((1 - -4)^2 + (1 - 1)^2)
= sqrt(5^2 + 0^2)
= sqrt(25 + 0)
= sqrt(25)
= 5
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: To find the shortest distance between Euclid Elementary School and Hypotenuse High School, we'll again use the distance formula.
Using the coordinates of Euclid Elementary School (x1, y1) = (-4, 1) and Hypotenuse High School (x2, y2) = (-4, -3), we have:
distance = sqrt((-4 - -4)^2 + (-3 - 1)^2)
= sqrt(0^2 + (-4)^2)
= sqrt(0 + 16)
= sqrt(16)
= 4
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: To find the shortest distance between Math Middle School and Hypotenuse High School, we'll once again apply the distance formula.
Using the coordinates of Math Middle School (x1, y1) = (1, 1) and Hypotenuse High School (x2, y2) = (-4, -3), we get:
distance = sqrt((-4 - 1)^2 + (-3 - 1)^2)
= sqrt(-5^2 + (-4)^2)
= sqrt(25 + 16)
= sqrt(41)
As the problem requests, we won't simplify the square root part.
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is sqrt(41) miles.
Part D: Comparing the distances traveled by both Deon and Kaya, we can determine who went the shortest distance.
Deon went from Hypotenuse High to Euclid Elementary (4 miles) and then to Math Middle (5 miles), for a total of 9 miles.
Kaya went directly from Hypotenuse High to Math Middle, with a distance of sqrt(41) miles.
Since sqrt(41) is approximately 6.4 miles, we can conclude that Kaya traveled the shortest distance.