P(3, 2) and Q(7, k) are the given points. If | 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 $P(3, 2)$,$Q(7,

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$5$

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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 $P(3, 2)$,$Q(7, k)$,and $d(P, Q) = 5$.Squaring both sides,we get $PQ^2 = 5^2 = 25$.Using the distance formula: $(7 - 3)^2 + (k - 2)^2 = 25$.$(4)^2 + (k - 2)^2 = 25$.$16 + (k - 2)^2 = 25$.$(k - 2)^2 = 25 - 16 = 9$.Taking the square root on both sides: $k - 2 = \pm 3$.Case $1$: $k - 2 = 3 \implies k = 5$.Case $2$: $k - 2 = -3 \implies k = -1$.Since $5$ is one of the options provided,the correct value is $k = 5$.

$P(3, 2)$ and $Q(7, k)$ are the given points. If $d(P, Q) = 5$,then $k = \dots \dots \dots$

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