Question

Which line is perpendicular to a line that has a slope of -1/3?

Answer 1

Answer:

Option (c)

Step-by-step explanation:

Slope of a line that passing through two points M(-1, 4) and N(2, -5),

$m_1$ = $\frac{y_2-y_1}{x_2-x_1}$

   = $\frac{-1-2}{4+5}$

   = -($\frac{3}{9}$)

   = -$\frac{1}{3}$

To find the line perpendicular line to MN we will use the property,

$m_1\times m_2=-1$

Where $m_1$ and $m_2$ are the slopes of two perpendicular lines.

Slope of line perpendicular to MN $(m_2)$ will be,

$-\frac{1}{3}\times m_2=-1$

$m_2=3$

Slope of line joining two points J(-3, -4) and K(3, -2),

Slope = $\frac{-4+2}{-3-3}=\frac{1}{3}$

Slope of line joining two points A(-3, 2) and B(3, 0)

Slope = $\frac{2-0}{-3-3}=-\frac{1}{3}$

Slope of the line joining points E(0, -3) and F(2, 3),

Slope = $\frac{-3-3}{0-2}$ = 3

Therefore, line EF is perpendicular to the line MN.

Option (c) is the answer.