If the distance between the points (2, -3) an | vedclass

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(B) The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given points are $(2,

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$1$

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(B) The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given points are $(2, -3)$ and $(5, b)$ with distance $d = 5$.Substituting the values into the formula:$5 = \sqrt{(5 - 2)^2 + (b - (-3))^2}$$5 = \sqrt{(3)^2 + (b + 3)^2}$Squaring both sides:$25 = 9 + (b + 3)^2$$16 = (b + 3)^2$Taking the square root on both sides:$b + 3 = \pm 4$Case $1$: $b + 3 = 4 \implies b = 1$Case $2$: $b + 3 = -4 \implies b = -7$Since $1$ is one of the given options,the correct value is $b = 1$.

If the distance between the points $(2, -3)$ and $(5, b)$ is $5,$ then $b = \ldots \ldots \ldots .$

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