Question

Consider the following statements related to slopes and angles of lines:
A. The equation of a line which passes through the point \((x_1,y_1)\) and has the slope \(m\) is \(y-y_1=m(x-x_1)\),
B. The angle \(\theta\) between the lines having slopes \(m_1\) and \(m_2\) is given by \(\tan\theta=\pm\dfrac{m_2-m_1}{1+m_1m_2}\),
C. The acute angle \(\theta\) between two lines \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) is given by \(\tan\theta=\left|\dfrac{a_2b_1-a_1b_2}{a_1a_2+b_1b_2}\right|\),
D. The equation of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(y-y_1=\left|\dfrac{y_2-y_1}{x_2-x_1}\right|(x-x_1)\).

• A. A, B
• B. A, B, C
• C. A, B, C, D
• D. B, C, D

Hint:

For straight-line questions, remember point-slope form, two-point form and angle formula using slopes.

Answer 1

The Correct Option is C