Question

Two points $(a,0)$ and $(0,b)$ are joined by a straight line. Another point on this line is

• A. $(3a,-2b)$
• B. $(a^2,ab)$
• C. $(-3a,2b)$
• D. $(a,b)$

Answer 1

The correct option is A $(3a,-2b)$

Given that $(a,0)$ and $(0,b)$ lie on a straight line.

We know that a straight line is represented by $y=mx+c$

Substituting co-ordinates in equation, we get

$\left(1\right)0=am+c$

$\left(2\right)b=a\left(0\right)+c=c$

$\Rightarrow m=\frac{-b}{a},c=b$

$\therefore$ Equation of line is $ay=ab-bx$

Substituting options we see that $(3a,-2b)$ lies on this line