If the mid-point of the line segment joining | vedclass

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(C) The mid-point formula for a line segment joining points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}).$Given p

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$7$

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(C) The mid-point formula for a line segment joining points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}).$Given points are $A (3, 4)$ and $B (k, 6).$Thus,the mid-point $P (x, y) = (\frac{3+k}{2}, \frac{4+6}{2}) = (\frac{3+k}{2}, 5).$Comparing the coordinates,we get $x = \frac{3+k}{2}$ and $y = 5.$We are given the equation $x+y-10=0.$Substituting the values of $x$ and $y$ into the equation:$\frac{3+k}{2} + 5 - 10 = 0$$\frac{3+k}{2} - 5 = 0$$\frac{3+k}{2} = 5$$3+k = 10$$k = 10 - 3$$k = 7.$

If the mid-point of the line segment joining the points $A (3, 4)$ and $B (k, 6)$ is $P (x, y)$ and $x+y-10=0,$ find the value of $k.$

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