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Given points A(1,2) and C(-1,-1), find the distance AC using the distance formula.

Mathematics

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a) (ii) Find AC
Given points: A(1,2)A(1,2) and C(−1,−1)C(-1,-1).
The distance formula is d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

  1. Substitute the coordinates of A and C into the distance formula.

    AC=(−1−1)2+(−1−2)2AC = \sqrt{(-1 - 1)^2 + (-1 - 2)^2}

  2. Calculate the differences.

    AC=(−2)2+(−3)2AC = \sqrt{(-2)^2 + (-3)^2}

  3. Square the differences.

    AC=4+9AC = \sqrt{4 + 9}

  4. Add the squared

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