Question

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 miles, from euclid elementary school to hypotenuse high school. show every step of your work. (2 points)
part c: use the pythagorean theorem to find the shortest distance, in miles, from math middle school to hypotenuse high school. show every step of your work. (4 points)
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. (4 points)

Explanation:

Part A:

Step1: Identify coordinates

Let Euclid Elementary be \((x_1,y_1)=(1, - 4)\) and Math Middle be \((x_2,y_2)=(1,1)\).

Step2: Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute \(x_1 = 1,y_1=-4,x_2 = 1,y_2 = 1\) into the formula:

$$
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$$

Part B:

Step1: Identify coordinates

Let Euclid Elementary be \((x_1,y_1)=(1,-4)\) and Hypotenuse High be \((x_2,y_2)=(-3,-4)\)

Step2: Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute \(x_1 = 1,y_1=-4,x_2=-3,y_2=-4\) into the formula:

$$
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$$

Part C:

Step1: Identify coordinates

Let Math Middle be \((x_1,y_1)=(1,1)\) and Hypotenuse High be \((x_2,y_2)=(-3,-4)\)

Step2: Find differences in \(x\) and \(y\)

\(\Delta x=x_2 - x_1=-3 - 1=-4\), \(\Delta y=y_2 - y_1=-4 - 1=-5\)

Step3: Apply Pythagorean theorem \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\)

$$
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$$

Part D:

Kaya's distance: \(d_{Kaya}=5\) (from Hypotenuse High to Math Middle).
Deon's distance: \(d_{Deon}=4 + 6.4=10.4\) (from Hypotenuse High to Euclid Elementary then to Math Middle).
Since \(5<10.4\), Kaya went the shortest distance.

Answer:

• Part A: \(5\) miles.
• Part B: \(4\) miles.
• Part C: \(\sqrt{41}\approx6.4\) miles.
• Part D: Kaya went the shortest distance.