Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade 11
Question:
$ABCD$ is rectangle with $A(-1,2)$, $B(3,7)$ and $AB : BC = 4:3$. If $d$ is the distance of origin from the intersection point of diagonals of rectangle, then possible values of $|d|$ is/are (where $[.]$ denote greatest integer function):
Step-by-Step Solution
Key Concept: The intersection point of diagonals in a quadrilateral can be found by setting parametric forms of the diagonal lines equal and solving for parameters.
For quadrilateral $ABCD$, compute $BC = \frac{3}{4}AB = \frac{3}{4}\sqrt{41}$. The perimeter is $p = \frac{1}{2}BC = \frac{3}{8}\sqrt{41}$ and $\tan\alpha = -\frac{4}{5}$. Find the intersection of diagonals using parametric equations of the lines containing each diagonal, yielding coordinates involving terms with $\sqrt{41}$.
Correct Answer: 2,4