If the distance between points A(a, 2) and B( | vedclass

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(C) 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 $A(a

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$a = 5$ or $a = 1$

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(C) 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 $A(a, 2)$ and $B(3, -5)$ with distance $d = \sqrt{53}$.Substituting the values into the formula:$\sqrt{(3 - a)^2 + (-5 - 2)^2} = \sqrt{53}$Squaring both sides:$(3 - a)^2 + (-7)^2 = 53$$(3 - a)^2 + 49 = 53$$(3 - a)^2 = 53 - 49$$(3 - a)^2 = 4$Taking the square root on both sides:$3 - a = 2$ or $3 - a = -2$If $3 - a = 2$,then $a = 1$.If $3 - a = -2$,then $a = 5$.Therefore,the possible values of $a$ are $1$ and $5$.

If the distance between points $A(a, 2)$ and $B(3, -5)$ is $\sqrt{53},$ find the possible values of $a$.

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