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?
options: -7, -5, 2, 3

Explanation:

Step1: Find slope of ST

Points \( S(-5, 0) \) and \( T(5, 2) \). Slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
\( m_{ST} = \frac{2 - 0}{5 - (-5)} = \frac{2}{10} = \frac{1}{5} \).

Step2: Find slope of VW (perpendicular)

Perpendicular slopes: \( m_1 \cdot m_2 = -1 \). Let \( m_{VW} = m \).
\( \frac{1}{5} \cdot m = -1 \Rightarrow m = -5 \).

Step3: Use point V and slope to find y

Point \( V(0, -2) \), point \( W(-1, y) \). Slope formula for VW:
\( -5 = \frac{y - (-2)}{-1 - 0} \Rightarrow -5 = \frac{y + 2}{-1} \).
Multiply both sides by -1: \( 5 = y + 2 \Rightarrow y = 3 \).

Answer:

3