Question:
ABCD is a rectangle where points C and D have coordinates (−2, 0) and (2, 0), respectively. If the area of the rectangle is 24, what is the best way to describe the equation of the line AB?
ABCD is a rectangle where points C and D have coordinates (−2, 0) and (2, 0), respectively. If the area of the rectangle is 24, what is the best way to describe the equation of the line AB?
Show Hint
For rectangles symmetric about the x-axis, the height determines the vertical location of lines parallel to the base. Use the area formula to calculate dimensions efficiently.
Updated On: Jan 5, 2025
- y = 3
- y = 6
- y = −3
- y = −6
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Understanding the Geometry of the Rectangle:
\(C\) and \(D\) are on the x-axis with coordinates \((-2, 0)\) and \((2, 0)\). The length of side \(CD\) (the base of the rectangle) is:
\[ \text{Length of } CD = |2 - (-2)| = 4 \]
Determine the Height of the Rectangle: The area of a rectangle is given by:
\[ \text{Area} = \text{Base} \times \text{Height} \]
Substituting the known values:
\[ 24 = 4 \times \text{Height} \]
\[ \text{Height} = \frac{24}{4} = 6 \]
Finding the Line \(AB\):
Since the height is perpendicular to \(CD\) and the rectangle is symmetric about the x-axis, the lines \(AB\) and \(CD\) are parallel. The line \(AB\) lies at a height of \(\frac{6}{2} = 3\) units above the x-axis. The equation of \(AB\) is:
\[ y = 3 \]
Thus, the best description of the equation of \(AB\) is \(y = 3\).
Was this answer helpful?
0
0
Top Questions on Geometry
- The distance of the point \( (7, 10, 11) \) from the line \( \frac{x-9}{2} = \frac{y-13}{3} = \frac{z-17}{6} \) along the line is:
- Let a circle \( C \) with radius \( r \) passes through four distinct points \( (0, 0), (k, 3k), (2, 3), (-1, 5) \), such that \( k \neq 0 \), then \( (10k + 2r^2) \) is equal to:
- A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?
- If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]
- The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
View More Questions
Questions Asked in XAT exam
- In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
- \(R\) and \(S\) scored the same on the first test.
- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
- XAT - 2025
- Algebra
- Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.
- XAT - 2025
- Analytical Decision Making
- There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.
- XAT - 2025
- Analytical Decision Making
- Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:Tasks:
A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns. - A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?
- XAT - 2025
- Percentage
View More Questions