Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade None
Question:
In a triangle $ABC$, if $A(2, -1)$ and $7x-10y+1=0$ and $3x-2y+5=0$ are equations of an altitude and an angle bisector respectively drawn from $B$, then equation of $BC$ is:
x + y + 1 = 0
5x + y + 17 = 0
4x + 9y + 30 = 0
x - 5y - 7 = 0
Step-by-Step Solution
Key Concept: The image of a point under reflection is found using the perpendicular foot as the midpoint between the original and image points.
To find the image of $A(2, -1)$ with respect to line $3x - 2y + 5 = 0$, use the reflection formula. The perpendicular from $A$ to the line has slope $-2/3$. Finding the foot of perpendicular and using the property that it's the midpoint of $A$ and $A'$ gives $A' = (-4, 3)$. The equation of line $BC$ passing through $B(-3, -2)$ and $A'(-4, 3)$ is $5x + y + 17 = 0$.
Correct Answer: 2