Question

determine if lines r and s are perpendicular. select the correct choice below and fill in the answer boxes to complete your choice.

Explanation:

Step1: Recall slope - perpendicularity rule

Two lines are perpendicular if the product of their slopes \(m_1\) and \(m_2\) is \(- 1\), i.e., \(m_1\times m_2=-1\).

Step2: Find the slope of line \(r\)

Suppose we can identify two points \((x_1,y_1)\) and \((x_2,y_2)\) on line \(r\). The slope \(m_r=\frac{y_2 - y_1}{x_2 - x_1}\).

Step3: Find the slope of line \(s\)

Suppose we can identify two points \((x_3,y_3)\) and \((x_4,y_4)\) on line \(s\). The slope \(m_s=\frac{y_4 - y_3}{x_4 - x_3}\).

Step4: Calculate the product of slopes

Multiply \(m_r\) and \(m_s\): \(m_r\times m_s\). If \(m_r\times m_s=-1\), the lines are perpendicular; if not, they are not.

Since the actual points on the lines are not given in the text - based description, we cannot calculate the final answer. But the general procedure to determine if two lines are perpendicular using the slope - product rule is as above. If we assume we have calculated the slopes of the two lines in the grid - based graph and found that the product of their slopes is \(-1\), then:

Answer:

The lines \(r\) and \(s\) are perpendicular. If the product is not \(-1\), the answer would be: The lines \(r\) and \(s\) are not perpendicular.