What is the shortest distance, in miles, between your home and the mall? Round to the nearest hundredth.

To find the shortest distance between your home and the mall, let’s first determine the coordinates of both locations:

1. Your home is at (0, 0).
2. The school is located 2 miles south of your home, which means its coordinates are (0, -2).
3. The mall is located 5 miles west of the school. Moving west affects the x-coordinate, so we subtract from the x-coordinate of the school:

– The mall’s coordinates will be (0 – 5, -2) = (-5, -2).

Now, we need to find the distance between your home (0, 0) and the mall (-5, -2). We can use the distance formula, which is:

[

d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

]

Substituting in the coordinates:

– Home (x1, y1) = (0, 0)

– Mall (x2, y2) = (-5, -2)

So we have:

[

d = sqrt{((-5) – 0)^2 + ((-2) – 0)^2}

]

Calculating that:

[

d = sqrt{(-5)^2 + (-2)^2} = sqrt{25 + 4} = sqrt{29}

]

Now we can calculate (sqrt