Find the equation of the line parallel to the line $x = 10$ and passing through the midpoint of the segment joining $( 9,7 )$ and $( 5 , - 3 )$.
A) $\quad y = 2$
B) $x = 7$
C) $x = 9$
D) $\quad x = 4$
E) $\quad y = - 5$

Question

Quizplus · Accepted Answer

The line $x = 10$ is a vertical line. A line parallel to it would also be a vertical line, which means its equation will be in the form $x = k$, where $k$ is a constant. To find the midpoint of the segment joining $(9,7)$ and $(5,-3)$, we use the midpoint formula: $\left(\frac{9+5}{2}, \frac{7+(-3)}{2}\right) = \left(\frac{14}{2}, \frac{4}{2}\right) = (7,2)$. The line passing through this midpoint and parallel to $x = 10$ will have the equation $x = 7$.

Find the Equation of the Line Parallel to the Line x=10x = 10x=10

Find the Equation of the Line Parallel to the Line $x = 10$