Open in App
Log In Start studying!

Select your language

Suggested languages for you:

If the points \((2 a, a),(a, 2 a)\) and \((a, a)\) enclose a triangle of area 18 sq. units, find the centroid of the triangle.

Short Answer

Expert verified
The centroid of the triangle is (2,2).
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Over 22 million students worldwide already upgrade their learning with Vaia!

Step 1: Formulating the Equation for the Area of the Triangle

The area of the triangle can be calculated using the formula Area = 1/2 |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|. Substituting the given points into the formula, we get 1/2 |2a(2a - a) + a(a - 2a) + a(a - 2a)| = 18.

Step 2: Solving for \(a\)

Solving this equation, we find that \(a\) equals 3 or -3. However, since \(a\) cannot be negative in this context, we conclude that \(a\) equals 3.

Step 3: Calculating the Centroid of the Triangle

The centroid of a triangle is calculated using the formula (x1+x2+x3/3, y1+y2+y3/3). Substituting the values of \(a\) and the coordinates, we get the centroid as (2,2).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 1

The equation of a circle \(C_{1}\) is \(x^{2}+y^{2}=4\). The locus of the intersection of orthogonal tangents to the circle is the curve \(C_{2}\) and the locus of the intersection of perpendicular tangents to the curve \(C_{2}\) is the curve \(C_{3}\). Then : (a) \(C_{3}\) is a circle (b) The area enclosed by the curve \(C_{3}\) is \(8 \pi\) (c) \(C_{2}\) and \(C_{3}\) are circles with the same centre (d) none of these

Chapter 1

Consider the circles and $$ \begin{aligned} &C_{1}=x^{2}+y^{2}-2 x-4 y-4=0 \\ &C_{2}=x^{2}+y^{2}+2 x+4 y+4=0 \end{aligned} $$ and the line \(L=x+2 y+2=0\). Then (a) \(L\) is the radical axis of \(C_{1}\) and \(C_{2}\) (b) \(L\) is the common tangent of \(C_{1}\) and \(C_{2}\) (c) \(L\) is the common chord of \(C_{1}\) and \(C_{2}\) (d) \(L\) is perpendicular to the line joining centres of \(C_{1}\) and \(C_{2}\)

Chapter 1

If \(A(a, a), B(-a,-a)\) are two vertices of an equilateral triangle, then its third vertex is: (a) \(\left(\frac{a \sqrt{3}}{2},-\frac{a \sqrt{3}}{2}\right)\) (b) \((-a \sqrt{3}, a \sqrt{3})\) (c) \((a \sqrt{3},-a \sqrt{3})\) (d) \((-a \sqrt{3},-a \sqrt{3})\)

Chapter 1

Find the equation of the pair of tangents from the origin to the circle \(x^{2}+y^{2}+2 g x+2 f y+\lambda^{2}=0\), and show that their intercept on the line \(y=h\) iss \(\frac{2 h \lambda}{\lambda^{2}-g^{2}}\) times the radius of the circle.

Chapter 1

Find the number of integral values of \(\lambda\) for which $x^{2}+y^{2}+\lambda x+(1-\lambda) y+5=0$ is the equation of a circle whose radius can not exceed \(\underline{5}\).

More chapters from the book ‘Skills in Mathematics for All Engineering Entrance Examinations: Coordinate Geometry’

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks