A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is
- 4units
- 8units
- 4√2units
- 2√2units
The Correct Option is A
Solution and Explanation
Given: The area of triangle \( \triangle ABC = 32 \, \text{square units} \), and side \( BC \) lies on the vertical line \( x = 4 \), with length \( 8 \) units.
To find the shortest distance between point \( A \) and the origin \( (0, 0) \), we start by using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, base \( BC = 8 \) units and the area is given as 32, so we plug in:
\[ 32 = \frac{1}{2} \times 8 \times \text{height} \]
Solving for height:
\[ \text{height} = \frac{32 \times 2}{8} = 8 \, \text{units} \]
Since line \( BC \) lies on the vertical line \( x = 4 \), any point directly above or below it forming the height must also lie on a vertical line.
Thus, point \( A \) must lie on a line parallel to \( BC \), also at \( x = 4 \), so A’s x-coordinate is 4.
The shortest distance from point \( A \) to the origin \( (0, 0) \) is the horizontal distance, since both points lie on vertical lines:
\[ \text{Distance} = |4 - 0| = 4 \, \text{units} \]
Therefore, the shortest possible distance between A and the origin is:
\[ \boxed{4 \text{ units}} \]
Top Questions on Mensuration
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Questions Asked in CAT exam
- The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
- Para Summary
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