Question

what can be concluded about the graphed polygon?
graph: coordinate plane with points (-2,4), (5,4), (5,-3), (-4,-3); sides labeled a, b, c, d
options:

• side a is parallel to line b.
• side a is parallel to line c.
• the slopes of sides d and c are reciprocals.
• the slope of side d is 0.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Calculate slope of side a

Points for side a: \((-2, 4)\) and \((5, 4)\).
Slope \( m_a=\frac{4 - 4}{5 - (-2)}=\frac{0}{7} = 0 \).

Step3: Calculate slope of side b

Points for side b: \((5, 4)\) and \((5, -3)\).
Slope \( m_b=\frac{-3 - 4}{5 - 5}=\frac{-7}{0} \) (undefined, vertical line).

Step4: Calculate slope of side c

Points for side c: \((-4, -3)\) and \((5, -3)\).
Slope \( m_c=\frac{-3 - (-3)}{5 - (-4)}=\frac{0}{9} = 0 \).

Step5: Calculate slope of side d

Points for side d: \((-4, -3)\) and \((-2, 4)\).
Slope \( m_d=\frac{4 - (-3)}{-2 - (-4)}=\frac{7}{2} \).

Step6: Analyze options

• Option 1: \( m_a = 0 \), \( m_b \) undefined. Not parallel.
• Option 2: \( m_a = 0 \), \( m_c = 0 \). Parallel (horizontal lines).
• Option 3: \( m_d=\frac{7}{2} \), \( m_c = 0 \). Not reciprocals.
• Option 4: \( m_d=\frac{7}{2}

eq0 \). False.

Answer:

Side a is parallel to line c.