Question

Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura’s place?

17 miles
24 miles
32 miles
36 miles

Answer 1

17 miles.

Explanation:

Let's define:

North as the positive y-axis

East as the positive x-axis.

We know that Laura lives 15 miles east of Kevin's place.

Kevin lives 8 miles south of Michelle's place.

So, if we define the origin, (0, 0) as Laura's place.

From:

"that Laura lives 15 miles east of Kevin's place."

We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:

(0, 0) + (-15mi, 0) = (-15mi, 0)

From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.

Then the location of Michele's house is the location of Kevin's plus (0, 8mi).

Michelle's house is located at:

(-15mi, 0) + (0, 8mi) =(-15mi, 8mi)

Now we want to find the distance between Michelle's house and Laura's house.

Michelle's house is at (-15mi, 8mi)

Laura's house is at (0mi, 0mi)

Remember that the distance between two points (a, b) and (c, d) is given by:

`D = √((a - c)^2 + (b - d)^2)`

Then the distance between (-15mi, 8mi) and (0mi, 0mi) is:

`D = √((-15mi - 0mi)^2 + (8mi - 0mi)^2) = 17mi`

The correct option is the first one, 17 miles.