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

Suppose your home is located at (0, 0) on a coordinate plane. The school is located 2 miles south of your home. The mall is located 5 miles west of the school. What is the shortest distance, in miles, between your home and the mall? Round to the nearest hundredth.




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  1. 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

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