Question

The image of the origin with respect to the line $4x+3y=25$, is

• A. (4, 3)
• B. (3, 4)
• C. (6, 8)
• D. (4, 6)
• E. (8, 6)

Answer 1

Answer: (E)

Let $Q\left(x_1,y_1\right)$ be the image of the point $P(0,0)$ in the line mirror $4x+3y-25=0$. Then, the coordinates of $Q$ are given by
$\frac{x_1-0}{4}=\frac{y_1-0}{3}=-\frac{2(4\times 0+3\times 0-25)}{25}$
$\Rightarrow \frac{x_1}{4}=\frac{y_1}{3}=\frac{-2(-25)}{25}\Rightarrow \frac{x_1}{4}=\frac{y_1}{3}=2$
$\Rightarrow x_1=8\text{ or }{y}_1=6$
Hence, the coordinates of image is $(8,6)$.