If the distance between the points (a, 1) and | 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,

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$5$

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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 $(a, 1)$ and $(8, a)$ with distance $d = 5$.Substituting the values into the formula:$5 = \sqrt{(8 - a)^2 + (a - 1)^2}$Squaring both sides:$25 = (8 - a)^2 + (a - 1)^2$$25 = (64 - 16a + a^2) + (a^2 - 2a + 1)$$25 = 2a^2 - 18a + 65$$2a^2 - 18a + 40 = 0$Dividing by $2$:$a^2 - 9a + 20 = 0$Factoring the quadratic equation:$(a - 4)(a - 5) = 0$Thus,$a = 4$ or $a = 5$.Since $5$ is one of the given options,the correct answer is $5$.

If the distance between the points $(a, 1)$ and $(8, a)$ is $5,$ then $a=$

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