Question

Find the slope and the inclination of the line AB if :

(i) A = (-3, -2) and B = (1, 2)

(ii) A = $(0,-\sqrt{3})$ and B = (3, 0)

(iii) A = $(-1,2\sqrt{3})$ and B = $(-2,\sqrt{3})$$\left[3Marks\right]$

Answer 1

(i) A = (-3, -2) and B = (1, 2)

Slope of AB = $\frac{2+2}{1+3}=1=tan\theta$

Inclination of line AB = $\theta$ = ${45}^{\circ }$$\left[1Mark\right]$

(ii) A = $(0,-\sqrt{3})$ and B = (3, 0)

Slope of AB = = $\frac{0+\sqrt{3}}{3-0}=\frac{1}{\sqrt{3}}=tan\theta$

Inclination of line AB = $\theta$ = ${30}^{\circ }$$\left[1Mark\right]$

(iii) A = $(-1,2\sqrt{3})$ and B = $(-2,\sqrt{3})$

Slope of AB = = $\frac{\sqrt{3}-2\sqrt{3}}{-2+1}=\sqrt{3}=tan\theta$

Inclination of line AB = $\theta$ = ${60}^{\circ }$$\left[1Mark\right]$