Chapter 3: Coordinate Geometry – Notes, Practice & Exercise Solutions (Class 9, NCERT/CBSE)
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Copy each section (1-mark → 2-mark → 3-mark → Exercises) into your site’s content area. Questions are red and solutions are green. MathJax renders all expressions crisply on mobile.
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1-Mark Questions (20)
1) What are the coordinate axes called?
Horizontal axis: \(x\)-axis; vertical axis: \(y\)-axis.
2) What is the origin?
The point of intersection of the axes; coordinates \((0,0)\).
3) Define abscissa and ordinate.
Abscissa = \(x\)-coordinate (distance from \(y\)-axis). Ordinate = \(y\)-coordinate (distance from \(x\)-axis).
4) Write the quadrant of the point \((4,-2)\).
IV quadrant \((+,-)\).
5) Coordinates of any point on the \(x\)-axis are of the form?
\((x,0)\).
6) Coordinates of any point on the \(y\)-axis are of the form?
\((0,y)\).
7) Which quadrant does \((-3,5)\) lie in?
II quadrant \((-,+)\).
8) Is \((3,4)=(4,3)\)?
No; order matters in ordered pairs.
9) What is the sign pattern in Quadrant III?
\((-,-)\).
10) Give the abscissa of \((-7,0)\).
\(-7\).
11) Give the ordinate of \((0,-6)\).
\(-6\).
12) Point \((5,0)\) lies in which quadrant?
On the \(x\)-axis (in no quadrant).
13) Write the coordinates of the reflection of \((a,b)\) in the \(x\)-axis.
\((a,-b)\).
14) Write the coordinates of the reflection of \((a,b)\) in the \(y\)-axis.
\((-a,b)\).
15) If the ordinate is \(0\), where does the point lie?
On the \(x\)-axis.
16) Write the coordinates of the point at distance \(4\) right of the origin on \(x\)-axis.
\((4,0)\).
17) State the coordinates of the origin.
\((0,0)\).
18) If a point is \((p,q)\) with \(p>0,q>0\), which quadrant?
I quadrant.
19) If a point is \((p,q)\) with \(p<0,q=0\), where is it?
On negative \(x\)-axis.
20) Write the ordered pair for column \(5\) and row \(3\) in a seating grid.
\((5,3)\) (column first, then row).
2-Mark Questions (20)
1) Write the quadrant (or axis) of each: \((3,7),\,(-4,2),\,(-5,-6),\,(0,-3)\).
I, II, III, on negative \(y\)-axis respectively.
2) Give the coordinates of points \(A,B,C,D\) on the \(x\)-axis at \(x=-4,-1,3,6\).
\(A(-4,0), B(-1,0), C(3,0), D(6,0)\).
3) Find the reflection of \((-8,5)\) in (i) \(x\)-axis (ii) \(y\)-axis.
(i) \((-8,-5)\) (ii) \((8,5)\).
4) If \(P(a,b)\) lies in Quadrant IV and \(Q(a,-b)\) is its reflection in the \(x\)-axis, what is the quadrant of \(Q\)?
Quadrant I (since \(a>0,\,-b>0\Rightarrow b<0\)).
5) A point is \(6\) units left of the \(y\)-axis and \(4\) units below the \(x\)-axis. Write its coordinates.
\((-6,-4)\).
6) Fill in the blank so that the point is on the \(y\)-axis: \((\_\_, -7)\).
\(0\). Point is \((0,-7)\).
7) Which of the following are in Quadrant II? \((2,-1),\,(-3,4),\,(-5,-6),\,(0,3)\).
Only \((-3,4)\).
8) If \(P(0,p)\) and \(Q(q,0)\), where do \(P\) and \(Q\) lie?
\(P\) lies on \(y\)-axis; \(Q\) lies on \(x\)-axis.
9) The point \(T\) has abscissa \(-5\) and ordinate \(2\). Write \(T\).
\(T(-5,2)\).
10) What is the sign of the ordinate for points in Quadrant IV?
Negative.
11) Find the coordinates of the reflection of \((m,n)\) in the origin.
\((-m,-n)\).
12) State whether each statement is true or false: (i) \((x,y)=(y,x)\) for all \(x,y\). (ii) Every point on \(x\)-axis has ordinate \(0\).
(i) False (only if \(x=y\)). (ii) True.
13) Find the coordinates of the midpoint of the segment joining \((0,0)\) and \((4,0)\) by observation from axes.
At \(x=2\) on \(x\)-axis: \((2,0)\). (Using symmetry on the axis; formal midpoint formula is not required here.)
14) Which axis (or quadrant) does the point \((k,0)\) lie on for (i) \(k<0\) (ii) \(k>0\)?
(i) Negative \(x\)-axis (ii) Positive \(x\)-axis.
15) For the grid “Street–House” system, which is correct: Street first or House first?
Street (like \(x\)-coordinate) first, then House (like \(y\)-coordinate).
16) Plot mentally: A point \(2\) left of \(y\)-axis and \(3\) above \(x\)-axis.
\((-2,3)\) in Quadrant II.
17) Name the quadrant of \((-7,0)\) and \((0,9)\).
\((-7,0)\): on negative \(x\)-axis; \((0,9)\): on positive \(y\)-axis.
18) If \(P\) lies on the line \(x=0\) and \(Q\) lies on the line \(y=0\), what are \(P\) and \(Q\)?
\(P\) is on \(y\)-axis; \(Q\) is on \(x\)-axis.
19) Write the coordinates of a point \(3\) units right and \(5\) units down from \((1,2)\).
\((1+3,\,2-5)=(4,-3)\).
20) If the abscissa is \(4\) and the ordinate is \(-6\), write the point.
\((4,-6)\).
3-Mark Questions (20)
1) Classify each point by quadrant/axis and write abscissa & ordinate: \((4,5),\,(-2,7),\,(-3,-1),\,(6,0),\,(0,-4)\).
I: \((4,5)\Rightarrow x=4,y=5\). II: \((-2,7)\Rightarrow x=-2,y=7\). III: \((-3,-1)\Rightarrow x=-3,y=-1\). On \(x\)-axis: \((6,0)\Rightarrow x=6,y=0\). On \(y\)-axis: \((0,-4)\Rightarrow x=0,y=-4\).
2) The reflection of \(A(3,-4)\) in the \(y\)-axis is \(A'\). Find \(A'\) and then reflect \(A'\) in the \(x\)-axis to get \(A''\).
\(A'( -3,-4)\); then \(A''(-3,4)\).
3) A rectangle has vertices \(P(-4,0),Q(2,0),R(2,3),S(-4,3)\). List the coordinates and identify sides parallel to axes.
Given vertices are correct. \(PQ\) & \(RS\) are on \(x\)-axis direction (horizontal). \(QR\) & \(SP\) are parallel to \(y\)-axis (vertical).
4) A point \(M\) is the reflection of \(N(-5,2)\) in the origin. Find \(M\) and its quadrant.
\(M(5,-2)\) in Quadrant IV.
5) Move from \(O(0,0)\) to \(A\) by “right 4, up 3”, then to \(B\) by “left 6, down 5”. Write \(A\) and \(B\).
\(A(4,3)\). From \(A\), \(B=(4-6,3-5)=(-2,-2)\).
6) The point \(T\) lies on \(x\)-axis and is equidistant from \(O\) and \(Q(6,0)\). Find \(T\).
Midway on \(x\)-axis: \(T(3,0)\).