Suggested languages for you:

Americas

Europe

Problem 25

If the square \(A B C D\) where \(A(0,0), B(2,0), C(2,2)\) and \(D(0,2)\) undergoes the following three transformations successively (i) \(f_{1}(x, y) \rightarrow(y, x)\) (ii) \(f_{2}(x, y) \rightarrow(x+3 y, y)\) (iii) \(f_{3}(x, y) \rightarrow\left(\frac{x-y}{2}, \frac{x+y}{2}\right)\) then the final figure is a : (a) square (b) parallelogram (c) rhombus (d) none of these

Expert verified

The final figure after applying all three transformations is none of the provided options.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- 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

Chapter 1

The centre of a circle which is orthogonal to the circles $C_{1}: x^{2}+y^{2}=25\( and \)C_{2}:(x-7)^{2}+(y-5)^{2}=4$ and which has the least radius is : (a) \(\left(5, \frac{25}{7}\right)\) (b) \((5,7)\) (c) \((7,12)\) (d) none of these

Chapter 1

If \(a, b, c\) are distinct real numbers, show that the points $\left(a, a^{2}\right),\left(b, b^{2}\right)\( and \)\left(c, c^{2}\right)$ are not collinear.

Chapter 1

Find the locus of the point of intersection of two perpendicular lines each of which touches one of the two circles \((x-a)^{2}+y^{2}=b^{2},(x+a)^{2}+y^{2}=c^{2}\) and prove that the bisectors of the angles between the straight lines always touch one or the other fixed circles.

Chapter 1

Let \(\mathrm{d}(P, O A) \leq \min \\{d(P, A B), d(P, B C), d(P, O C)\\}\) where \(d\) denotes the distance from the point to the corresponding line and \(S\) be the region consisting of all those points \(P\) inside the rectangle \(O A B C\) such that \(O=(0,0), A=(3,0), B=(3,2)\) and \(C=(0,2)\), which satisfy the above relation, then area of the region \(S\) is : (a) 2 (b) 3 \(\angle\) (c) 4 (d) none of these

Chapter 1

\(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) are the ends of a diameter of a circle such that \(x_{1}\) and \(x_{2}\) are the roots of $a x^{2}+b x+c=0\( and \)y_{1}\( and \)y_{2}\( are the roots of \)a_{1} y^{2}+b_{1} y+c_{1}=Q$ Find the equation of the circle and also find its centre and radius.

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