CHAPTER 7 : COORDINATE GEOMETRY
CBSE Class 10 Mathematics — PYQs 2026 | Basic + Standard
BASIC QUESTION PAPER 2026
SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)
A. Abscissa and Ordinate
1.
For a point
(3, −5), the value of
(abscissa − ordinate) is:
(A) −8
(B) −2
(C) 2
(D) 8
[Set 430/1/1 Q.5]
B. Distance from Coordinate Axes
2.
The distance of a point
P(3, −7)
from the y-axis is:
(A) 3
(B) 7
(C) −7
(D) √58
[Set 430/1/2 Q.17]
3.
The distance of the point
(−3, 4)
from the y-axis is:
(A) −3
(B) 3
(C) 4
(D) 5
[Sets: 430/3/1 Q.7, 430/3/2 Q.1, 430/3/3 Q.12]
4.
For a point
X(a, b)
where
b > a > 0,
the value of
distance from x-axis − distance from y-axis
is:
(A) a − b
(B) b − a
(C) a² − b²
(D) b² − a²
[Set 430/1/3 Q.10]
C. Distance from Origin
5.
The distance of the point
(2, 3)
from the origin is:
(A) 2
(B) 3
(C) 5
(D) √13
[Sets: 430/2/1 Q.6, 430/2/3 Q.11]
D. Mid-point Formula
6.
The mid-point of a line segment divides the line segment in the ratio:
(A) 1 : 2
(B) 2 : 1
(C) 1 : 1
(D) 1/2 : 2
[Sets: 430/1/1 Q.6, 430/1/2 Q.18, 430/1/3 Q.11]
7.
The mid-point of the line segment joining the points
(1, 3)
and
(1, −3)
lies:
(A) at the origin
(B) in the second quadrant
(C) on x-axis
(D) on y-axis
[Sets: 430/2/1 Q.7, 430/2/2 Q.1, 430/2/3 Q.12]
8.
If point
(1, 2)
is the mid-point of the line segment joining the points
(3, 5)
and
(2a, b),
then
(a, b)
is:
(A) (−1, −1)
(B) (−1/2, −1/2)
(C) (−1/2, −1)
(D) (−1, −1/2)
[Set 430/3/1 Q.6]
9.
If point
(a, 2b)
is the mid-point of the line segment joining the points
(3, 5)
and
(−1, −1),
then
(a, b)
is equal to:
(A) (1, 1)
(B) (2, 2)
(C) (2, 1)
(D) (1, 1)
Note: Options (A) and (D) are identical in the source text.
[Set 430/3/3 Q.11]
SECTION B : CASE STUDY BASED QUESTIONS (4 Marks Each)
Type A : Circular Park and Section Formula
10.
Case Study: The Circular Park Gates
A circular park has two gates at
A(10, 20)
and
B(50, 50).
Two fountains
P and
Q
are installed on
AB such that
AP = PQ = QB.
(i) [1 Mark]
Find the coordinates of the centre C.
(ii) [1 Mark]
Find the radius of the circular park.
(iii) [2 Marks]
(a) Find the coordinates of point
P.
OR
(b) Find the distance of the fountain at
Q
from gate
A.
[Sets: 430/1/1 Q.38, 430/1/2 Q.37, 430/1/3 Q.36]
Type B : Rectangular Field and Diagonals
11.
Case Study: The Rectangular Field Race
A rectangular field
ABCD has coordinates
A(10, 10),
B(40, 10),
C(40, 50)
and
D(x, y).
Anita runs along diagonal
AC to intersection point
E, then to
B along diagonal
DB.
Anil runs from
C to
A
via
D.
(i) [1 Mark]
Find the coordinates of point E.
(ii) [1 Mark]
Find the distance between points B and
C.
(iii) [2 Marks]
(a) Find the coordinates of point
D
and the distance
BD.
OR
(b) Find the total distance travelled by Anita.
[Sets: 430/2/1 Q.38, 430/2/2 Q.37, 430/2/3 Q.36]
Type C : Mid-point and Section Formula
12.
Case Study: The Semicircular Park Borewell
A semicircular park has a diameter
AB with
A(2, 3) and B(22, 3).
There is a borewell at the centre
O.
(i) [1 Mark]
Find the coordinates of point O.
(ii) [1 Mark]
Find the radius of the semicircular park.
(iii) [2 Marks]
(a) One sapling is kept at point
C(12, y).
Find the coordinates of
C.
OR
(b) Find coordinates of point
P along
AB so that
PA = 1/3 PB.
[Sets: 430/3/1 Q.38, 430/3/2 Q.37, 430/3/3 Q.36]
STANDARD QUESTION PAPER 2026
SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)
A. Distance Formula Applications
1.
The distance between the points
(a cos θ + b sin θ, 0)
and
(0, a sin θ − b cos θ)
is:
(A) √(a² + b²)
(B) a² − b²
(C) √(a² − b²)
(D) a² + b²
[Set 30/4/1 Q.15, Set 30/4/3 Q.1]
2.
The distance of the point
A(4a, 3a)
from the x-axis is:
(A) 3a
(B) −3a
(C) 4a
(D) −4a
[Set 30/2/1 Q.9, Set 30/2/3 Q.1]
3.
If the distance between the points
(4, p)
and
(1, 0)
is 5, then
p is equal to:
(A) ±4
(B) 4
(C) −4
(D) 0
[Set 30/2/2 Q.10]
B. Section Formula and Mid-point
4.
The line segment joining the points
P(−4, −2)
and
Q(10, 4)
is divided by the y-axis in the ratio:
(A) 2 : 5
(B) 1 : 2
(C) 2 : 1
(D) 5 : 2
[Set 30/5/1 Q.2, Set 30/5/2 Q.8, Set 30/5/3 Q.7]
5.
The mid-point of the line segment joining the points
(5, −4)
and
(6, 4)
lies on:
(A) x-axis
(B) y-axis
(C) origin
(D) neither x-axis nor y-axis
[Set 30/1/1 Q.8, Set 30/1/2 Q.9, Set 30/1/3 Q.6]
SECTION B : VERY SHORT ANSWER QUESTIONS (2 Marks Each)
A. Triangle and Collinearity
6.
Do the points
P(1, 0),
Q(−5, 0)
and
R(−2, 5)
form a triangle?
If so, name the type of triangle formed.
[Set 30/1/3 Q.21]
7.
Using distance formula, prove that the points
A(2, 3), B(−7, 0) and C(−1, 2)
are collinear.
[Set 30/5/1 Q.22(b), Set 30/5/2 Q.25(b), Set 30/5/3 Q.22(b)]
8.
Vertices of a right triangle
ABC
with
∠B = 90°
are
A(3, 4), B(1, 1) and C(−8, 7).
Find the value of
tan A.
[Set 30/5/1 Q.22(a), Set 30/5/2 Q.25(a)]
B. Circle and Coordinate Applications
9.
The coordinates of the centre of a circle are
(x − 7, 2x).
Find the value(s) of
x, if the circle passes through
the point
(−9, 11)
and has radius
5√2 units.
[Set 30/1/1 Q.23, Set 30/1/2 Q.22]
10.
In the given figure, point
D divides the side
BC of
ΔABC
in the ratio 1 : 2.
Given:
A(1, 5), B(−2, 1), C(4, 2)
Find the length of
AD.
[Set 30/5/3 Q.21]
11.
If the points
A(4, 5),
B(m, 6),
C(4, 3)
and
D(1, n)
taken in this order are the vertices of a parallelogram
ABCD,
find the values of
m and
n.
[Set 30/2/1 Q.23, Set 30/2/2 Q.25]
SECTION C : SHORT ANSWER QUESTIONS (3 Marks Each)
A. Ratio and Section Formula
12.
Find the ratio in which the x-axis divides the line segment joining the points
(−6, 5) and (−4, −1).
Also, find the point of intersection.
[Set 30/1/1 Q.27, Set 30/1/3 Q.31]
13.
Find the coordinates of the points of trisection of the line segment joining the points
A(−1, 4) and B(−3, −2).
[Set 30/2/1 Q.27, Set 30/2/2 Q.30]
14.
A point
P divides the line segment joining the points
A(−3, 5) and B(7, −4)
in a certain ratio. If point
P lies on the line
y = 2x,
find the ratio
AP : PB
and the coordinates of point
P.
[Set 30/3/2 Q.27]
15.
Determine the ratio in which the line
3x + y − 9 = 0
divides the line segment joining the points
(1, 3) and (2, 5).
Find the point of intersection.
[Set 30/3/3 Q.28]
B. Circles and Chords
16.
A circle centred at
(2, 1)
passes through the points
A(5, 6)
and
B(−3, K).
Find the value(s) of
K.
Hence, find the length of chord
AB.
[Set 30/5/1 Q.29(a), Set 30/5/3 Q.26(a)]
17.
Prove that the point
P dividing the line segment
joining the points
A(−1, 7) and B(4, −3)
in the ratio 3 : 2, lies on the line
x − 3y = −1.
Also find the lengths of
PA and
PB.
[Set 30/5/1 Q.29(b), Set 30/5/3 Q.26(b)]
SECTION D : CASE STUDY BASED QUESTION (4 Marks)
Type A : Coordinate Geometry in a City Map
18.
Case Study: The Jaipur City Map
Taking Rambagh Palace as the origin
(0, 0),
the locations of different places are represented by the following points:
A(−4, 2) — Rajasthan High Court
B(4, −4) — Birla Mandir
C(4, 3) — Heera Bagh
D(−5, −2) — Amar Jawan Jyoti
(i) [1 Mark]
Advocate Rehana stays at Heera Bagh.
How much distance does she have to cover daily to go to the court
and come back home?
(ii) [1 Mark]
There is a crossing on the x-axis which divides
AD
in a certain ratio.
Find the ratio.
(iii) [2 Marks]
(a) Is Birla Mandir equidistant from Heera Bagh and
Amar Jawan Jyoti? Justify your answer.
OR
(b) Using section formula, show that points
A, O and
B
are not collinear.
[Sets: 30/4/1 Q.38, 30/4/2 Q.37, 30/4/3 Q.37]