Question

Please Help!!

(Pythagorean Theorem and the Coordinate Plane HC)
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 milles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work. (2 points)
Part C: Find the shortest distance, In milles, 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

To find the shortest distances between the schools, use the Pythagorean Theorem on the coordinate plane.

Step-by-step explanation:

The shortest distance between two points can be found using the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Part A: The distance from Euclid Elementary School (-3, 5) to Math Middle School (5, 5) can be found using the formula: distance = √((x2 - x1)² + (y2 - y1)²).

Calculate the horizontal distance: x2 - x1 = 5 - (-3) = 8

Calculate the vertical distance: y2 - y1 = 5 - 5 = 0

Use the formula: distance = √(8² + 0) = √64 = 8 miles

Part B: The distance from Euclid Elementary School (-3, 5) to Hypotenuse High School (-3, -2) can be found using the same formula.

Calculate the horizontal distance: x2 - x1 = -3 - (-3) = 0

Calculate the vertical distance: y2 - y1 = -2 - 5 = -7

Use the formula: distance = √(0² + (-7)²) = √49 = 7 miles

Part C: The distance from Math Middle School (5, 5) to Hypotenuse High School (-3, -2) can also be found using the same formula.

Calculate the horizontal distance: x2 - x1 = -3 - 5 = -8

Calculate the vertical distance: y2 - y1 = -2 - 5 = -7

Use the formula: distance = √((-8)² + (-7)²) = √113 = 10.6 miles

Answer 2

The shortest distance from Euclid Elementary to Math Middle is 8 miles, to Hypotenuse High it's 7 miles, and from Math Middle to Hypotenuse High it's 7 miles. Braylen traveled the shortest overall distance, taking a straight line of 7 miles, while Javi traveled a total of 15 miles.

Step-by-step explanation:

The problem requires us to apply the Pythagorean Theorem on a coordinate plane to find the shortest distances between the schools.

Part A: Euclid Elementary to Math Middle School

Both schools are located at y=5, so we can find the distance by subtracting their x-coordinates. The distance is |5 - (-3)| = 8 miles.

Part B: Euclid Elementary to Hypotenuse High School

The two schools form a vertical line on the graph, so the distance is the difference in their y-coordinates: |5 - (-2)| = 7 miles.

Part C: Math Middle School to Hypotenuse High School

The distance between these two schools is the hypotenuse c of the right triangle with legs a and b. Here, a = |5 - 5| = 0 miles and b = |5 - (-2)| = 7 miles. Thus, we calculate c = √(0² + 7²) = √49 = 7 miles.

Part D: Comparing Distances Traveled

Javi went from Hypotenuse High to Euclid Elementary to Math Middle which is 7 miles + 8 miles = 15 miles. Braylen traveled directly from Hypotenuse High to Math Middle School which is a straight line and the shortest distance found in Part C, 7 miles. Therefore, Braylen went the shortest distance.