Find the angle between two straight lines with slopes m1 = 2 and m2 = -3.
Answer and explanation
Correct answer: D. 45 degrees (pi/4)
- Step 1: Tan theta formula: tan(theta) = |(m1 - m2) / (1 + m1 m2)|. Step 2. tan(theta) = |(2 - (-3)) / (1 + (2)(-3))| = |5 / (1 - 6)| = |5 / (-5)| = |-1| = 1. Step 3. theta = arctan(1) = 45 degrees. Answer: 45 degrees (pi/4). Why not the others: Lines are perpendicular (90°) when m1m2 = -1; here m1*m2 = -6.
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