Question

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Explanation:

Step1: Find equation of Line A

Using point-slope form \( y - y_1 = m(x - x_1) \):
\( y - 6 = -\frac{2}{5}(x - 2) \)
Simplify: \( y = -\frac{2}{5}x + \frac{4}{5} + 6 = -\frac{2}{5}x + \frac{34}{5} \)

Step2: Find equation of Line B

Using point-slope form:
\( y - (-2) = \frac{1}{3}(x - (-33)) \)
Simplify: \( y + 2 = \frac{1}{3}x + 11 \) → \( y = \frac{1}{3}x + 9 \)

Step3: Set equations equal to solve for x

\( -\frac{2}{5}x + \frac{34}{5} = \frac{1}{3}x + 9 \)
Multiply by 15 to eliminate denominators:
\( -6x + 102 = 5x + 135 \)
\( -11x = 33 \) → \( x = -3 \)

Step4: Find y using Line B's equation

\( y = \frac{1}{3}(-3) + 9 = -1 + 9 = 8 \)

Answer:

A. \( x = -3, y = 8 \)