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SAT Math Difficulty: Hard (800) • Calibrated to 2026 Testing Standard

Digital SAT Math Practice Question #881

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(-4, 2) $ and $ B(6, 8) $. 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 $?

Select Your Answer:

Socratic AI Engine Step-by-Step Derivation

0ms Precomputed

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(-4, 2) $ and $ B(6, 8) $. Use midpoint formula to plot $ M(1, 5) $. Enter $ y - 5 = 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 $: \[ M = \left(\frac{-4 + 6}{2}, \frac{2 + 8}{2}\right) = (1, 5) \] Step 2: Find the slope of segment $ AB $: \[ m_{AB} = \frac{8 - 2}{6 - -4} = 0.60 \] Step 3: The perpendicular bisect...

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

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