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

$(3a,–2b)$

The explanation for the correct answer.

Solve for the required point.

Let $A(a,0)$and$B(0,b)$ be the points.

Slope of $AB,m=-\frac{b}{a}$

Equation of line is $y–y_1=m(x–x_1)$

$$\begin{gathered} \Rightarrow y-0=\left(-\frac{b}{a}\right)\left(x-a\right) \\ \Rightarrow ay+bx=ab \\ \Rightarrow \frac{x}{a}+\frac{y}{b}=1...\left(i\right) \end{gathered}$$

Substitute given options in $\left(i\right)$ and check.

Check option $\left(1\right).$

$$\begin{gathered} \frac{3a}{a}–\frac{2b}{b}=1 \\ \Rightarrow 3–2=1 \end{gathered}$$

Hence, option(A) is the correct answer.