Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.
-
A.
40° -
B.
44° -
C.
45° -
D.
54°
Correct Answer: Option C
Explanation
(2x + y = 4 equiv y = 4 – 2x implies m_{1} = -2)
(-3x + y + 7 = 0 equiv y = -7 + 3x implies m_{2} = 3)
(tan theta = frac{m_{1} – m_{2}}{1 – m_{1}m_{2}} = frac{-2 – 3}{1 – (-2)(3)} = frac{-5}{-5} = 1)
(tan theta = 1 implies theta = 45°)