Question

line st and point v are shown on the graph. line vw is to be drawn on the graph such that it is perpendicular to line st. if the coordinates of point w are (-1, y), what is the value of y?

Explanation:

Find coordinates of S and T

Using the Slope Formula knowledge point

$$ S = (-5, 0),\quad T = (5, 2) $$

Calculate slope of line ST

Using the Slope Formula knowledge point

$$ m_{ST} = \frac{2 - 0}{5 - (-5)} = \frac{2}{10} = \frac{1}{5} $$

Determine slope of perpendicular line VW

The slope of a perpendicular line is the negative reciprocal of the original slope.

$$ m_{VW} = -\frac{1}{m_{ST}} = -5 $$

Set up slope equation for line VW

Using the Slope Formula knowledge point

$$
LATEXBLOCK0
$$

Solve for y

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) -7
• (B) -5
• (C) 2
• (D) 3 (Correct answer)