ACT Math Practice Question #1287 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1287

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What is the area, in square units, of the triangle in the standard $(x,y)$-coordinate plane with vertices at $(0, 0)$, $(6, 2)$, and $(4, 8)$?
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Shoelace from origin: $|6(8) - 4(2)| / 2 = (48 - 8)/2 = 20$.

Masterclass Solution & Distractor Trap Analysis

Use the shoelace formula for a triangle with one vertex at the origin $(0, 0)$ and points $(x_1, y_1)$ and $(x_2, y_2)$: $$\text{Area} = \frac{1}{2}|x_1 y_2 - x_2 y_1|.$$ Substitute $(6, 2)$ and $(4, 8)$: $$\text{Area} = \frac{1}{2}|(6)(8) ...

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

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