Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade 11
Question:
Suppose that a ray of light leaves the point $(3, 4)$, reflects off the $y$-axis towards the $x$-axis, reflects off the $x$-axis, and finally arrives at the point $(8, 2)$. The value of $x$ is:
x = 4\frac{1}{2}
x = 4\frac{1}{3}
x = 4\frac{2}{3}
x = 5\frac{1}{3}
Step-by-Step Solution
Key Concept: Use equal ratios (collinearity condition) to solve for the unknown coordinate of a point on a line.
Simplify the equation $\frac{0+2}{x-8} = \frac{4+2}{-3-8} = \frac{6}{-11}$ to get $\frac{2}{x-8} = -\frac{6}{11}$. Cross-multiplying: $2 \cdot 11 = -6(x - 8)$, which gives $22 = -6x + 48$, so $6x = 26$ and $x = \frac{13}{3}$.
Correct Answer: 2