Straight Lines
Image of a Point
JEE Main 2020
Grade 11
Question:
The line in the $xy$-plane with $x$-intercept 3 and $y$-intercept 1 is $x + 3y = 3$. The image of the point $(-1, -4)$ in this line is:
(1) $\left(\frac{29}{5}, \frac{11}{5}\right)$
(2) $\left(\frac{11}{5}, \frac{28}{5}\right)$
(3) $\left(3, \frac{5}{2}\right)$
(4) $\left(\frac{5}{3}, \frac{13}{3}\right)$
Step-by-Step Solution
Key Concept: For the image of $(x_1, y_1)$ in $ax + by + c = 0$: $\frac{h-x_1}{a} = \frac{k-y_1}{b} = \frac{-2(ax_1+by_1+c)}{a^2+b^2}$. Apply with $a = 1, b = 3, c = -3$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)