Find the tangent to the acute angle between the lines 2x + y = 3 and 3x – 2y = 5.
-
A.
-7/4 -
B.
7/8 -
C.
7/4 -
D.
7/2
Correct Answer: Option C
Explanation
Let (phi) be the angle between the two lines.
tan (phi) = (frac{m_1 – m_2}{1 + m_1 m_2})
where m(_1) = slope of line 1; m(_2) = slope of line 2.
Line 1: 2x + y = 3 (implies) y = 3 – 2x.
Line 2: 3x – 2y = 5 (implies) -2y = 5 – 3x.
y = (frac{3}{2})x – (frac{5}{2}).
m(_1) = -2, m(_2) = (frac{3}{2}).
tan (phi) = (frac{-2 – frac{3}{2}}{1 + (-2 times frac{3}{2})})
= (frac{frac{-7}{2}}{-2})
(therefore) Tan (phi) = (frac{7}{4}).