Question:
The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is
Updated On: Sep 26, 2024
- -5
- -6
- -7
- -8
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is (D):
In a rectangle, diagonals bisect each other, so one diagonal should pass through the midpoint of the other. Midpoint of the diagonal connecting (2, 5) and (6, 3)
= (2+6/2, 5+3/2) = (4,4)
The other diagonal, y = 3x + c should also pass through (4, 4).
On substitution, 4 = 3 (4) + c ⇒ –8.
Was this answer helpful?
0
0
Top Questions on Geometry
- 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?
- 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?
- The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:
- The points A(4, -2, 1), B(7, -4, 7), C(2, -5, 10), and D(-1, -3, 4) are the vertices of a:
- If A, B, C, D are the angles of a quadrilateral, then \[ \frac{\tan A + \tan B + \tan C + \tan D}{\cot A + \cot B + \cot C + \cot D} = \]
View More Questions
Questions Asked in CAT exam
- For any natural Number 'n', let an be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =
- CAT - 2024
- Number Systems
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- In September, the incomes of \(K\), \(A\), and \(V\) are in the ratio \(8:6:5\). They rent a house, contributing \(15\%\), \(12\%\), and \(18\%\) of their respective incomes. In October, the rent remains the same, but the salaries of \(K\), \(A\), and \(V\) increase by \(10\%\), \(12\%\), and \(15\%\), respectively. What percentage of their total income is paid as house rent in October? (Round to the nearest percentage.)
- CAT - 2024
- Percentages
View More Questions