Question

The graph of $f\left(x\right)$ is shown above in the $xy$-plane. The points $(0,3),(5b,b)$ and $(10b,-b)$ are on the line described by $f\left(x\right)$. If $b$ is a positive constant, find the coordinates of point $C$.

• A. $(5,1)$
• B. $(10,-1)$
• C. $(15,-0.5)$
• D. $(20,-2)$

Answer 1

The correct option is B $(10,-1)$

In given figure the line goes to point $A(0,3),B(5b,b)$ and $C(10b,-b)$

Then slope of line goes at point $A(0,3)$ and $B(5b,b)=$ $\frac{b-3}{5b-0}=\frac{b-3}{5b}$

And slope of line goes at point $B(5b,b)$ and $C(10b,-b)=$ $\frac{-b-b}{10b-5b}=\frac{-2b}{5b}$

Then given line is a st reline then both slopes are equal

$\therefore \frac{b-3}{5b}=\frac{-2b}{5b}$

$\Rightarrow -2b=b-3$

$\Rightarrow -3b=-3$

$\Rightarrow b=1$

Put the value of $b=1$ in point C

We get $C=(10,-1)$