Question

The acute angle between the line x + y = 3 and the line joining the points (1, 1) and (–3, 4) is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let A ≡ (1, 1) and B ≡ (–3, 4)

$\therefore$ Slope of AB, $m_1=\frac{1-4}{1+3}=-\frac{3}{4}$

Given line is x + y = 3

$\therefore$ Slope of given line, $m_2=-\frac{1}{1}=-1$

If $\theta$ is the acute angle between the two lines, then

$tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=\left|\frac{-\frac{3}{4}+1}{1+\frac{3}{4}}\right|=\frac{1}{7}\therefore \theta =ta{n}^1\left(\frac{1}{7}\right)$