Straight Lines
Straight Line
star_batch_jee_advanced_2025
Grade 11
Question:
In a $\triangle ABC$ equation of median and altitude from vertex $C$ and $B$ are $x + 2 = 0$ and $x + y - 2 = 0$ respectively, vertex $A$ is at the origin, then:
coordinate of point B is (-4,6)
equation of AC is x - y = 0
Area of triangle ABC is 10 square units
vertex C is (-2,-3)
Step-by-Step Solution
Key Concept: Using perpendicularity condition $m_1 \cdot m_2 = -1$ and point constraints to determine coordinates of vertices.
Given line $x + 2 = 0$ containing point $C$ with x-coordinate $-2$, we find $m_{AC} \cdot m_{BD} = -1$ implies $m_{AC} = 1$, so equation of $AC$ is $y = x$. Point $C$ is at $(-2, -2)$ and $D$ is at $(1, 1)$. If slope of $AB$ is $m$, then $B(-4, -4m)$ lies on $x + y - 2 = 0$, giving $-4 - 4m - 2 = 0$, so $m = - rac{3}{2}$. The coordinate of $B$ is $(-4, 6)$.
Correct Answer: 1,2,3