Questions: P(2,-1), Q(-3,-1), R(-11,9), S(-7,9)

Transcript text: P(2,-1), Q(-3,-1), R(-11,9), S(-7,9)

Solution

Solution Steps

Step 1: Calculate the slope of \(\overline{\mathrm{PQ}}\)

The slope \(m\) of a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

For \(\overline{\mathrm{PQ}}\), the points are \(P(2, -1)\) and \(Q(-3, -1)\). Plugging these into the formula:

\[ m(\overline{\mathrm{PQ}}) = \frac{-1 - (-1)}{-3 - 2} = \frac{0}{-5} = 0 \]

Step 2: Calculate the slope of \(\overline{\mathrm{RS}}\)

For \(\overline{\mathrm{RS}}\), the points are \(R(-11, 9)\) and \(S(-7, 9)\). Plugging these into the formula:

\[ m(\overline{\mathrm{RS}}) = \frac{9 - 9}{-7 - (-11)} = \frac{0}{4} = 0 \]

Step 3: Determine the types of lines

Both \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{RS}}\) have a slope of \(0\), which means they are horizontal lines.

Final Answer

\[ \begin{array}{|l|l|l|} \hline \boldsymbol{m}(\overline{\mathrm{PQ}}) & \mathbf{m}(\overline{\mathrm{RS}}) & \text{Types of Lines} \\ \hline 0 & 0 & \text{Horizontal Lines} \\ \hline \end{array} \]

\[ \boxed{ \begin{array}{|l|l|l|} \hline \boldsymbol{m}(\overline{\mathrm{PQ}}) & \mathbf{m}(\overline{\mathrm{RS}}) & \text{Types of Lines} \\ \hline 0 & 0 & \text{Horizontal Lines} \\ \hline \end{array} } \]

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