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Calculating the Distance Between Two Points

Find the distance between the points (-5, -10) and (2, 4).

4.58
12.12
15.65
21




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1 Answer

  1. To find the distance between the points (-5, -10) and (2, 4), we can use the distance formula:

    [

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

    ]

    Where ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).

    Now, let’s plug in the values:

    1. Calculate (x_2 – x_1):

    [

    2 – (-5) = 2 + 5 = 7

    ]

    2. Calculate (y_2 – y_1):

    [

    4 – (-10) = 4 + 10 = 14

    ]

    3. Substitute these into the distance formula:

    [

    d = sqrt{(7)^2 + (14)^2}

    ]

    [

    d = sqrt{49 + 196}

    ]

    [

    d = sqrt{245}

    ]

    [

    d approx 15.65

    ]

    So, the distance between the two points is approximately 15.65.

  2. To find the distance between the points ((-5, -10)) and ((2, 4)), we can use the distance formula:

    [

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

    ]

    Where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points.

    1. Here, ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).
    2. Calculate the differences:

    – (x_2 – x_1 = 2 – (-5) = 2 + 5 = 7)

    – (y_2 – y_1 = 4 – (-10) = 4 + 10 = 14)

    3. Now plug these values into the formula:

    [

    d = sqrt{(7)^2 + (14)^2} = sqrt{49 + 196} = sqrt{245}

    ]

    4. Finally, simplify (sqrt{245}):

    [

    sqrt{245} = sqrt{49 times 5} = 7sqrt{5} approx 15.65

    ]

    Therefore, the distance between the points

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