Question

Help! Please!! It's timed! I'll give brainliest!!

Answer 1

The distances are given as follows:

a) Euclid Elementary School to Math Middle School: 6 miles.

b) Euclid Elementary School to Hypotenuse High School: 7 miles.

c) Math Middle School to Hypotenuse High School: 9.2 miles.

d) Kaya went the shortest distance.

What is the distance between two points?

Suppose that we have two points with coordinates $(x_1,y_1)$ and $(x_2,y_2)$. The shortest distance between them is given by the following rule:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

For item a, the coordinates are given as follows:

• Euclid: (-2, 4).

• Math: (4,4).

Hence the distance in units is:

$D = \sqrt{(4-(-2))^2+(4-4)^2} = 6$

Each unit is one mile, hence 6 miles.

For item b, the coordinates are given as follows:

• Euclid: (-2, 4).

• Hypotenuse: (-2,-3).

$D = \sqrt{(-2-(-2))^2+(4-(-3))^2} = 7$

Hence 7 miles.

For item c, the coordinates are given as follows:

• Math: (4, 4).

• Hypotenuse: (-2,-3).

$D = \sqrt{(4-(-2))^2+(4-(-3))^2} = 9.2$

Hence 9.2 miles.

For item d, the distances are:

• Deon: 7 + 6 = 13 miles.

• Kaya: 9.2 miles.

9.2 < 13, hence Kaya went the shortest distance.

More can be learned about the distance between two points at brainly.com/question/18345417

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