NCERT Solutions Class 9 Maths Chapter One: Important Questions.
NCERT Class 9 Maths, Chapter 1 depends on your textbook edition. In the newer Ganita Manjari book, Chapter 1 is “Orienting Yourself: The Use of Coordinates.” Here are important questions with solutions.
1. What are the coordinates of the origin?
The two axes meet at \((0,0)\).
2. Are \(M(-3,-4)\), \(A(0,0)\), and \(G(6,8)\) on one straight line?
Yes. From \(M\) to \(A\), the changes are \((3,4)\). From \(A\) to \(G\), they are \((6,8)=2(3,4)\). Both segments have the same direction.
3. \(M(-7,1)\) is the midpoint of \(A(3,-4)\) and \(B(x,y)\). Find \(B\).
\[
\frac{3+x}{2}=-7 \quad\Rightarrow\quad x=-17
\]
\[
\frac{-4+y}{2}=1 \quad\Rightarrow\quad y=6
\]
Answer: \(B(-17,6)\).
4. \(A(1,-8)\), \(B(-4,7)\), and \(C(-7,-4)\) lie on a circle centred at the origin. Find its radius.
Each point is \(\sqrt{65}\) units from \((0,0)\). For example:
\[
OA=\sqrt{1^{2}+(-8)^{2}}=\sqrt{65}.
\]
Radius: \(\sqrt{65}\) units. \(D(-5,6)\) is inside the circle because its distance from the origin is \(\sqrt{61}\). \(E(0,9)\) is outside because its distance is \(9\).
5. Is \(A(2,1)\), \(B(-1,2)\), \(C(-2,-1)\), \(D(1,-2)\) a square? Find its area.
All four sides have length \(\sqrt{10}\). Adjacent sides are perpendicular because:
\[
(-3)(-1)+(1)(-3)=3-3=0.
\]
It is a square; its area is \(10\) square units.
Source: NCERT Chapter 1.
