Question

Lines $L$ and $M$ are perpendicular to each other. Line $L$ has an undefined slope. Find the possible equation of line $M$.

• A. $x=y$
• B. $y=7$
• C. $x=-3$
• D. $xy=4$

Answer 1

Answer: (B)

$y=7$

Let $L$ and $M$ be two lines which are perpendicular to each other.

Slope of line is given by $m=\frac{y_2-y_1}{x_2-x_1}$

$m$ is undefined, if denominator becomes zero i.e if the value of $x$-coordinate remains same at every point.

$\because L$ has undefined slope

$⟹$ value of $x$-coordinate remains same at every point lies on $L$

$⟹$ $L$ is a line parallel to $Y$-axis and thus, its a vertical line.

Vertical and horizontal lines are perpendicular to each other.

$\therefore$ The line $M$ which is perpendicular to line $L$ will be parallel to $X$-axis.

$\therefore$ $y$-coordinate will be constant at every point lies on $M$.

$\therefore m=0$ for $M$.

Hence, $y=7$ is the possible equation of line $M$.