Question

Line g passes through points (2, 14) and (8, 7). Line h passes through points (1, 1) and (8, 7). Are line g and line h parallel or perpendicular?

answer options:
1. parallel
2. perpendicular
3. neither

Answer 1

To determine whether lines g and h are parallel, perpendicular, or neither, we need to find the slopes of both lines.

**Step 1: Find the slope of line g.**
Line g passes through points (2, 14) and (8, 7).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points into the formula:
\[
m_g = \frac{7 - 14}{8 - 2} = \frac{-7}{6}
\]

So, the slope of line g is \( m_g = -\frac{7}{6} \).

**Step 2: Find the slope of line h.**
Line h passes through points (1, 1) and (8, 7).

Using the same formula:
\[
m_h = \frac{7 - 1}{8 - 1} = \frac{6}{7}
\]

So, the slope of line h is \( m_h = \frac{6}{7} \).

**Step 3: Determine the relationship between the slopes.**
For lines to be parallel, their slopes must be equal. For them to be perpendicular, the product of their slopes must equal -1.

Calculate the product of the slopes:
\[
m_g \times m_h = \left(-\frac{7}{6}\right) \times \left(\frac{6}{7}\right) = -1
\]

Since the product of the slopes is -1, this means the lines are perpendicular.

**Final Answer:**
The answer is **2. perpendicular**.