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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 (-2,6). Math middle school is graphed at (6,6). Find the distance, in miles, from Euclid Elementary School to math middle school. Show every step of your work

User Shemogumbe
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2 Answers

3 votes

Answer:

Step-by-step explanation:

Part A: Euclid Elementary School to Math Middle School To find the distance between two points ( x 1 , y 1 ) (x 1 ​ ,y 1 ​ ) and ( x 2 , y 2 ) (x 2 ​ ,y 2 ​ ) on a coordinate plane, you can use the distance formula: Distance = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Distance= (x 2 ​ −x 1 ​ ) 2 +(y 2 ​ −y 1 ​ ) 2 ​ For Euclid Elementary School ( − 4 , 1 ) (−4,1) and Math Middle School ( 1 , 1 ) (1,1): Distance = ( 1 − ( − 4 ) ) 2 + ( 1 − 1 ) 2 Distance= (1−(−4)) 2 +(1−1) 2 ​ Distance = 5 2 + 0 2 Distance= 5 2 +0 2 ​ Distance = 25 Distance= 25 ​ Distance = 5 miles Distance=5miles So, the shortest distance is 5 miles. Part B: Euclid Elementary School to Hypotenuse High School For Euclid Elementary School ( − 4 , 1 ) (−4,1) and Hypotenuse High School ( − 4 , − 3 ) (−4,−3): Distance = ( − 3 − 1 ) 2 + ( ( − 4 ) − ( − 4 ) ) 2 Distance= (−3−1) 2 +((−4)−(−4)) 2 ​ Distance = ( − 4 ) 2 + 0 2 Distance= (−4) 2 +0 2 ​ Distance = 16 Distance= 16 ​ Distance = 4 miles Distance=4miles So, the shortest distance is 4 miles. Part C: Math Middle School to Hypotenuse High School For Math Middle School ( 1 , 1 ) (1,1) and Hypotenuse High School ( − 4 , − 3 ) (−4,−3): Distance = ( − 3 − 1 ) 2 + ( ( − 4 ) − 1 ) 2 Distance= (−3−1) 2 +((−4)−1) 2 ​ Distance = ( − 4 ) 2 + ( − 5 ) 2 Distance= (−4) 2 +(−5) 2 ​ Distance = 16 + 25 Distance= 16+25 ​ Distance = 41 Distance= 41 ​ So, the shortest distance is 41 41 ​ miles. Part D: Deon vs. Kaya Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. The total distance is the sum of the distances found in Part B and Part A: Total distance for Deon = 4 + 5 = 9 miles Total distance for Deon=4+5=9miles Kaya traveled from Hypotenuse High to Math Middle along a straight path, as per Part C: Distance for Kaya = 41 miles Distance for Kaya= 41 ​ miles Therefore, Kaya went the shortest distance ( 41 41 ​ miles) compared to Deon (9 miles).

sorry its so long lol

User GreyBow
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5 votes

Final answer:

To find the distance between Euclid Elementary School and Math Middle School, we can use the distance formula. The distance is 8 miles.

Step-by-step explanation:

To find the distance between Euclid Elementary School and Math Middle School, we can use the distance formula. The distance formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) are the coordinates of Euclid Elementary School and (x2, y2) are the coordinates of Math Middle School.

Substituting the coordinates into the formula, we get:

d = sqrt((6 - (-2))^2 + (6 - 6)^2) = sqrt(64) = 8 miles.

User Kamil Szostakowski
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