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? -7 -5 2 3

Explanation:

Step1: Find the slope of line ST

Let \(S(-5,0)\) and \(T(5,2)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So, \(m_{ST}=\frac{2 - 0}{5-(-5)}=\frac{2}{10}=\frac{1}{5}\).

Step2: Find the slope of line VW

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line \(VW\) be \(m_{VW}\). Then \(m_{ST}\times m_{VW}=-1\). Since \(m_{ST}=\frac{1}{5}\), we have \(\frac{1}{5}\times m_{VW}=-1\), so \(m_{VW}=-5\).

Step3: Use the slope - formula for line VW

Let \(V(0,-2)\) and \(W(-1,y)\). Using the slope formula \(m_{VW}=\frac{y - (-2)}{-1 - 0}\). Since \(m_{VW}=-5\), we have \(\frac{y + 2}{-1}=-5\).

Step4: Solve for y

Cross - multiply: \(y + 2=5\). Subtract 2 from both sides: \(y=3\).

Answer:

3