Question

which point is on the line that passes through point h and is perpendicular to line fg?

\\((-6, 10)\\)
\\((-2, -12)\\)
\\((0, -2)\\)
\\((4, 2)\\)

Explanation:

Identify the coordinates of the given points

Using the Slope of a Line knowledge point

$$
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$$

Calculate the slope of line FG

Using the Slope of a Line knowledge point

$$ m_{FG} = \frac{4 - (-8)}{8 - (-8)} = \frac{12}{16} = \frac{3}{4} $$

Determine the perpendicular slope

Using the Perpendicular Line Equations knowledge point

$$ m_{\perp} = -\frac{1}{m_{FG}} = -\frac{4}{3} $$

Write the equation of the perpendicular line

Using the Point-Slope Form and Perpendicular Line Equations knowledge points

$$
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Test the given options

Using the Perpendicular Line Equations knowledge point

$$
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$$

Answer:

• (A) \((-6, 10)\) (Correct answer)
• (B) \((-2, -12)\)
• (C) \((0, -2)\)
• (D) \((4, 2)\)