ACT Math Practice Question #1231 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1231

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In the standard $(x,y)$-coordinate plane, the line $3x - 4y = 12$ is perpendicular to the line passing through points $(2, -1)$ and $(5, k)$. What is the value of $k$?
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Perpendicular slope is $-4/3$. Since denominator $(5 - 2) = 3$, numerator $(k + 1)$ must equal $-4 \implies k = -5$.

Masterclass Solution & Distractor Trap Analysis

Rewrite $3x - 4y = 12$ in slope-intercept form: $-4y = -3x + 12 \implies y = \frac{3}{4}x - 3$. The slope of this line is $m_1 = \frac{3}{4}$. The slope of a perpendicular line must be the negative reciprocal: $m_2 = -\frac{4}{3}$. The slop...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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