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.
To find the shortest distance between two points in the coordinate plane, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Part A: Finding the shortest distance from Euclid Elementary School to Math Middle School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Math Middle School: (1, 1)
Distance = sqrt((1 - (-4))^2 + (1 - 1)^2)
= sqrt(5^2 + 0^2)
= sqrt(25)
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: Finding the shortest distance from Euclid Elementary School to Hypotenuse High School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - (-4))^2)
= sqrt((-4)^2 + 0^2)
= sqrt(16)
= 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: Finding the shortest distance from Math Middle School to Hypotenuse High School.
Coordinates of Math Middle School: (1, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - 1)^2)
= sqrt((-4)^2 + (-5)^2)
= sqrt(16 + 25)
= sqrt(41)
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is sqrt(41) miles.
Part D: Comparing the distances traveled by Deon and Kaya.
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.
We can compare the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = sqrt(41) miles
Therefore, Kaya traveled the shortest distance because sqrt(41) is less than 9.
bot could you repeat everything you just said but take out sqrt
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School, we can use the distance formula:
Distance = √((1 - (-4))^2 + (1 - 1)^2)
= √(5^2 + 0^2)
= √25
= 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 use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - (-4))^2)
= √((-4)^2 + 0^2)
= √16
= 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 use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - 1)^2)
= √((-4)^2 + (-5)^2)
= √(16 + 25)
= √41 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is √41 miles.
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. Comparing the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = √41 miles
Therefore, Kaya traveled the shortest distance because √41 is less than 9.
repeat everything you just said but take out the checkmarks and don't add sqrt
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School, we can use the distance formula:
Distance = ((1 - (-4))^2 + (1 - 1)^2)
= (5^2 + 0^2)
= 25
= 25 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 25 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - (-4))^2)
= ((-4)^2 + 0^2)
= 16
= 16 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 16 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - 1)^2)
= ((-4)^2 + (-5)^2)
= 41
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 41 miles.
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. Comparing the distances:
Deon's distance = 16 + 25 = 41 miles
Kaya's distance = 41 miles
Therefore, Deon and Kaya traveled the same distance, which is 41 miles.
are you sure this is right?
I apologize for the incorrect responses in my previous answer. Let me correct them:
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School:
Distance = |1 - (-4)| + |1 - 1|
= 5 + 0
= 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:
Distance = |-3 - (-4)| + |-4 - 1|
= 1 + 5
= 6 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 6 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School:
Distance = |-3 - 1| + |-4 - 1|
= 4 + 5
= 9 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 9 miles.
Part D: Comparing the distances traveled by Deon and Kaya:
Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle: 6 + 5 = 11 miles.
Kaya traveled from Hypotenuse High to Math Middle along a straight path: 9 miles.
Therefore, Kaya traveled the shortest distance, which is 9 miles.