Which expression gives the distance between the points (1,-2) and (2,4) A. sqrt ((1+2)^2+(2-4)^2) B (1-2)^2+(-2-4)^2 c (1+2)^2+(2-4)^2 D. sqrt ((1-2)^2+(-2-4)^2)

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Which expression gives the distance between the points (1,-2) and (2,4) A. sqrt ((1+2)^2+(2-4)^2) B (1-2)^2+(-2-4)^2 c (1+2)^2+(2-4)^2 D. sqrt ((1-2)^2+(-2-4)^2)

Answer 1

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by the formula:\[\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]For the points \((1,-2)\) and \((2,4)\), we have:\[x_1 = 1, y_1 = -2, x_2 = 2, y_2 = 4\]Plugging these values into the distance formula:\[\text{Distance} = \sqrt{(2 - 1)^2 + (4 - (-2))^2}\]\[\text{Distance} = \sqrt{(1)^2 + (6)^2}\]\[\text{Distance} = \sqrt{1 + 36}\]\[\text{Distance} = \sqrt{37}\]The correct expression that gives the distance between the points is:D. \(\sqrt{(1-2)^{2}+(-2-4)^{2}}\)

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Which expression gives the distance between the points (1,-2) and (2,4) A. sqrt ((1+2)^2+(2-4)^2) B (1-2)^2+(-2-4)^2 c (1+2)^2+(2-4)^2 D. sqrt ((1-2)^2+(-2-4)^2)

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