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Calculate the distance between the points A(-12, 2) and B(-10, 0).

Mathematics

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Answer

222\sqrt{2}

Step-by-step solution

7 steps

  1. Identify the given points.

    The two points are A=(−12,2)A = (-12, 2) and B=(−10,0)B = (-10, 0).
    Let (x1,y1)=(−12,2)(x_1, y_1) = (-12, 2) and (x2,y2)=(−10,0)(x_2, y_2) = (-10, 0).

  2. Recall the distance formula between two points.

    The distance dd between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:

    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

  3. Substitute the coordinates of points A and B into the distance formula.

    d=(−10−(−12))2+(0−2)2d = \sqrt{(-10 - (-12))^2 + (0 - 2)^2}

  4. Simplify the terms inside the parentheses.

    d=(−10+12)2+(−2)2d = \sqrt{(-10 + 12)^2 + (-2)^2} d=(2)2+(−2)2d = \sqrt{(2)^2 + (-2)^2}

  5. Calculate the squares.

    d=4+4d = \sqrt{4 + 4}

  6. Add the terms under the square root.

    d=8d = \sqrt{8}

  7. Simplify the square root.

    d=4×2d = \sqrt{4 \times 2} d=4×2d = \sqrt{4} \times \sqrt{2} d=22d = 2\sqrt{2}

    The length of the straight line segment AB is 222\sqrt{2} units.

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