Find the value of k,if the line joining the p | vedclass

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(C) Let the points be $A(2, k)$,$B(3, 7)$,$C(-2, 1)$,and $D(3, 0)$.Since the line $AB$ is parallel to the line $CD$,their slopes must be equal,i.e.,$m

Vedclass · Accepted Answer

$\frac{36}{5}$

Vedclass · Answer

(C) Let the points be $A(2, k)$,$B(3, 7)$,$C(-2, 1)$,and $D(3, 0)$.Since the line $AB$ is parallel to the line $CD$,their slopes must be equal,i.e.,$m_{AB} = m_{CD}$.The slope of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$.$m_{AB} = \frac{7 - k}{3 - 2} = \frac{7 - k}{1} = 7 - k$.$m_{CD} = \frac{0 - 1}{3 - (-2)} = \frac{-1}{3 + 2} = \frac{-1}{5}$.Equating the slopes: $7 - k = \frac{-1}{5}$.$35 - 5k = -1$.$5k = 36$.$k = \frac{36}{5}$.

Find the value of $k$,if the line joining the points $(2, k)$ and $(3, 7)$ is parallel to the line joining points $(-2, 1)$ and $(3, 0)$.

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