If the mid-point of the line joining $(3, 4)$ and $(k, 7)$ is $(x, y)$ and $2x + 2y + 1 = 0$ find the value of $k$.

Given:

The mid-point of the line joining $(3, 4)$ and $(k, 7)$ is $(x, y)$ and $2x + 2y + 1 = 0$.

To do:

We have to find the value of $k$.

Solution:

Mid-point of the line joining the points $(3, 4)$ and $(k, 7)$ is $(x, y)$.

Therefore,

Using mid-point formula, we get,

\( x=\frac{3+k}{2} \) and \( y=\frac{4+7}{2} \)

\( \Rightarrow y=\frac{11}{2} \)
\( 2 x+2 y+1=0 \)               (Given)
\( \Rightarrow 2\left(\frac{3+k}{2}\right)+2 \times \frac{11}{2}+1=0 \)
\( \Rightarrow 3+k+11+1=0 \)

\( \Rightarrow k+15=0 \)
\( \Rightarrow k=-15 \)

The value of $k$ is \( -15 \).

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Updated on: 10-Oct-2022

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