Question:
Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is
Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is
Updated On: July 22, 2025
\(\frac{25}{4\sqrt3}\)
\(\frac{25\sqrt3}{2}\)
\(\frac{25}{\sqrt3}\)
\(\frac{25}{2\sqrt3}\)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is (D) : \(\frac{25}{2\sqrt3}\)
Altitude of equilateral triangle,
\(\frac{\sqrt3l}{2}=\frac{5}{\sqrt2}\)
\(l=\frac{5\sqrt2}{\sqrt3}\)
Area of triangle
\(=\frac{\sqrt3}{4}l^2=\frac{\sqrt3}{4}.\frac{50}{3}=\frac{25}{2\sqrt3}\)
Was this answer helpful?
0
0
Top Questions on Coordinate Geometry
- The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is:
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
- In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
- The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
- The area of a triangle with vertices at points $ A(1,2) $, $ B(4,6) $, and $ C(k, 8) $ is 5. Find the value of $ k $.
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
- If the distance between the points \( (2, -1) \) and \( (k, 3) \) is 5, then the possible values of \( k \) are:
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
View More Questions
Questions Asked in JEE Main exam
- If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:
- JEE Main - 2025
- Matrices and Determinants
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
- JEE Main - 2025
- Kinetic Energy
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- permutations and combinations
- A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
- JEE Main - 2025
- Magnetic Field
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
View More Questions
JEE Main Notification
GMC Azamgarh Admission 2025: Dates, Courses, Fees, Eligibility, SelectJuly 22, 2025GMC Azamgarh Admission 2025
Concepts Used:
Coordinate Geometry
Coordinate geometry, also known as analytical geometry or Cartesian geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent geometric figures and solve problems using algebraic equations and coordinate systems.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.