Question:
The area bounded by the lines $y - 2x = 2$, $y = 4$ and the y-axis is equal to (in square units):
The area bounded by the lines $y - 2x = 2$, $y = 4$ and the y-axis is equal to (in square units):
Show Hint
Whenever region is bounded by straight lines, always check if it forms a triangle — much faster than integration.
Updated On: May 2, 2026
- $1$
- $4$
- $0$
- $3$
- $2$
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The Correct Option is A
Solution and Explanation
Concept:
The region bounded by straight lines can be interpreted as a triangle.
Find the vertices using intersections, then apply:
\[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Step 1: Find the vertices of the region.
Given: \[ y = 2x + 2, \quad y = 4, \quad x = 0 \] Intersection with y-axis: \[ x=0 \Rightarrow y=2 \Rightarrow (0,2) \] Intersection of \( y=4 \) with y-axis: \[ (0,4) \] Intersection of \( y=2x+2 \) and \( y=4 \): \[ 4 = 2x + 2 \Rightarrow x = 1 \Rightarrow (1,4) \]
Step 2: Determine base and height.
Base (along \( y=4 \)): \[ \text{Length} = 1 - 0 = 1 \] Height (along \( x=0 \)): \[ \text{Length} = 4 - 2 = 2 \]
Step 3: Calculate area.
\[ \text{Area} = \frac{1}{2} \times 1 \times 2 = 1 \]
Step 4: Final answer.
\[ \boxed{1} \]
Step 1: Find the vertices of the region.
Given: \[ y = 2x + 2, \quad y = 4, \quad x = 0 \] Intersection with y-axis: \[ x=0 \Rightarrow y=2 \Rightarrow (0,2) \] Intersection of \( y=4 \) with y-axis: \[ (0,4) \] Intersection of \( y=2x+2 \) and \( y=4 \): \[ 4 = 2x + 2 \Rightarrow x = 1 \Rightarrow (1,4) \]
Step 2: Determine base and height.
Base (along \( y=4 \)): \[ \text{Length} = 1 - 0 = 1 \] Height (along \( x=0 \)): \[ \text{Length} = 4 - 2 = 2 \]
Step 3: Calculate area.
\[ \text{Area} = \frac{1}{2} \times 1 \times 2 = 1 \]
Step 4: Final answer.
\[ \boxed{1} \]
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