Question

which point on the \\(y\\)-axis lies on the line that passes through point \\(c\\) and is perpendicular to line \\(ab\\)?

\\((-6, 0)\\)
\\((0, -6)\\)
\\((0, 2)\\)
\\((2, 0)\\)

Explanation:

Find coordinates of points A, B, and C

Using the Slope of a Line knowledge point

$$ A = (-2, 4),\quad B = (2, -8),\quad C = (6, 4) $$

Calculate the slope of line AB

Using the Slope of a Line knowledge point

$$ m_{AB} = \frac{-8 - 4}{2 - (-2)} = \frac{-12}{4} = -3 $$

Determine the perpendicular slope

Using the Perpendicular Line Equations knowledge point

$$ m_{\perp} = -\frac{1}{m_{AB}} = -\frac{1}{-3} = \frac{1}{3} $$

Find the equation of the perpendicular line

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK0
$$

Find the y-intercept of the perpendicular line

Using the Perpendicular Line Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

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