Question

If the points (1,2) and (3,4) were to be on the same side of the line 3x-5y+a=0 then

• A. 7<a<11
• B. 7<a<11
• C. a=11
• D. a<7 or a>11

Answer 1

The correct option is D

a<7 or a>11

The points \( (x_1,y_1) \space and \space (x_2,y_2)\) lie on the same side of the line L=0 if $L_{11}.L_{22}$ >0 Here L=3x−5y+a=0

⇒ (3−10+a)(9−20+a)>0

⇒ (a−7)(a−11)>0 ⇒ a<7 or a>11