Determine graphically the vertices of the triangle formed by the lines $y = x$, $3y = x$ and $x + y = 8$.
Step-by-Step Solution
Key Concept: Line 1 $y = x$, Line 2 $x = 3y$, Line 3 $x + y = 8$. Intersection 1 & 2: $(0,0)$. Intersection 1 & 3: $x + x = 8 \Rightarrow (4,4)$. Intersection 2 & 3: $3y + y = 8 \Rightarrow y = 2, x = 6 \Rightarrow (6,2)$. Vertices: $(0,0), (4,4), (6,2)$.
Solve $y = x$ and $3y = x \Rightarrow (0,0)$. [1.0 Mark]
Solve $y = x$ and $x + y = 8 \Rightarrow 2x = 8 \Rightarrow (4,4)$. [1.0 Mark]
Solve $x = 3y$ and $x + y = 8 \Rightarrow 4y = 8 \Rightarrow (6,2)$. Vertices: $(0,0), (4,4), (6,2)$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding origin vertex $(0,0)$: 1.0 Mark
Finding vertex $(4,4)$: 1.0 Mark
Finding vertex $(6,2)$: 1.0 Mark
Correct Answer: