SAT Math Practice Question #882 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #882

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-2, -3) \) and \( B(4, 9) \). The perpendicular bisector of segment \( AB \) can be written in the form \( y = mx + b \), where \( m \) and \( b \) are constants. What is the value of \( m + b \)?
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Socratic AI Engine Step-by-Step Derivation
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Tactical Insight (Hint 1)

A perpendicular bisector passes through the segment's midpoint and has a slope that is the negative reciprocal of the segment's slope.

Elimination Framework (Hint 2)

Desmos Shortcut: Plot \( A(-2, -3) \) and \( B(4, 9) \). Use midpoint formula to plot \( M(1, 3) \). Enter \( y - 3 = m(x - 1) \) and adjust \( m \) until the line is perpendicular to segment \( AB \).

Masterclass Solution & Distractor Trap Analysis

Step 1: Find the midpoint \( M \) of segment \( AB \): \[ M = \left(\frac{-2 + 4}{2}, \frac{-3 + 9}{2}\right) = (1, 3) \] Step 2: Find the slope of segment \( AB \): \[ m_{AB} = \frac{9 - -3}{4 - -2} = 2.00 \] Step 3: The perpendicular bise...

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

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