Question

which point could be on the line that is parallel to line kl and passes through point m?
○ (-10, 0)
○ (-6, 2)
○ (0, -6)
○ (8, -10)

Explanation:

Step1: Find slope of KL

Points \( K(-6, 8) \) and \( L(6, 0) \). Slope \( m_{KL} = \frac{0 - 8}{6 - (-6)} = \frac{-8}{12} = -\frac{2}{3} \). Parallel lines have same slope, so new line has \( m = -\frac{2}{3} \). Point \( M(-4, -2) \).

Step2: Use point - slope form

Equation: \( y - (-2) = -\frac{2}{3}(x - (-4)) \), so \( y + 2 = -\frac{2}{3}(x + 4) \).

Step3: Test each option

• For \( (-10, 0) \): \( 0 + 2 = -\frac{2}{3}(-10 + 4) \Rightarrow 2 = -\frac{2}{3}(-6) \Rightarrow 2 = 4 \) (False).
• For \( (-6, 2) \): \( 2 + 2 = -\frac{2}{3}(-6 + 4) \Rightarrow 4 = -\frac{2}{3}(-2) \Rightarrow 4 = \frac{4}{3} \) (False).
• For \( (0, -6) \): \( -6 + 2 = -\frac{2}{3}(0 + 4) \Rightarrow -4 = -\frac{8}{3} \) (False).
• For \( (8, -10) \): \( -10 + 2 = -\frac{2}{3}(8 + 4) \Rightarrow -8 = -\frac{2}{3}(12) \Rightarrow -8 = -8 \) (True).

Answer:

\( (8, -10) \)