Table of contents  
Previous Year Questions 2024  
Previous Year Questions 2023  
Previous Year Questions 2022  
Previous Year Questions 2021  
Previous Year Questions 2020  
Previous Year Questions 2019 
Q1: Assertion (A): The point which divides the line segment joining the points A (1, 2) and B (–1, 1) internally in the ratio 1 : 2 is
Reason (R): The coordinates of the point which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m_{2} are (2024)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Ans: (d)
Assertion says that point
divides the line joining the points A(1, 2) and B(–1, 1) in 1 : 2.
∴ By section formula,
Q2: Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). (2024)
Ans:
Since, P(x, y) is equidistant from A(7, 1) and B(3, 5)
So, PA = PB
⇒ PA^{2} = PB^{2}
⇒ (x – 7)^{2} + (y – 1)^{2} = (x – 3)^{2} + (y – 5)^{2}
⇒ x^{2} + 49 – 14x + y^{2} + 1 – 2y = x^{2} + 9 – 6x + y^{2} + 25 – 10y
⇒ 6x – 14x + 50 – 34 + 10y – 2y = 0
⇒ – 8x + 8y + 16 = 0
⇒ 8x – 8y – 16 = 0
⇒ 8(x – y – 2) = 0
⇒ x – y – 2 = 0
⇒ x – y = 2
Q3: Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle. (2024)
Ans: A (– 1, y); B(5, 7)
Since, AB is a diameter of circle and O is the centre of the circle.
OA = OB i.e., O divides AB in 1 : 1
So m_{1} : m_{2} = 1 : 1
So
⇒
⇒ – 6y = y + 7
⇒ – 7y = 7
⇒ y = – 1
Point O = (2, 3), A = (–1, – 1)
Now,
So, radius of circles = 5 units
Q4: Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Yaxis. (2024)
Ans:
If yaxis divides points (5, 3) and (–1, 6) then coordinate of that point will be (0, y). Let P(0, y) divides A(5, 3) and B(–1, 6) in k : 1.
m_{1} : m_{2} = k : 1
⇒ 0 × (k + 1) = – k + 5
⇒ 0 = – k + 5
⇒ k = 5
So, m_{1} : m_{2} = 5 : 1
Ans: (b)
Distance from xaxis = ycoordinate of point = 7 units
Q6: Assertion (A): Point P(0, 2) is t be point of intersection of yaxis with the line 3x + 2y = 4. (2023)
Reason (R): The distance of paint P(0, 2) from xaxis is 2 units.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Ans: (b)
Point P(0, 2) is the point of intersection of yaxis with line 3x + 2y = 4
Also, the distance of point P(0, 2) from xaxis is 2 units.
Q7: The distance of the point (6, 8) from origin is (2023)
(a) 6
(b) 6
(c) 8
(d) 10
Ans: (d)
Distance of the point (6, 8) from origin (0, 0)
= 10 Units
Q8: The points (4, 0), (4, 0) and (0, 3) are the vertices of a (2023)
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
Ans: (b)
The points be A(4, 0), B(4, 0) and C(0, 3).
Using distance formula
= 8 units
= 5 units
= 5 units
And, AB^{2} ≠ BC^{2} + CA^{2 } [∵ BC = CA]
∴ ΔABC is an isosceles triangle.
Q9: The centre of a circle is (2a, a  7). Find the values of 'a' if the circle passes through the point (11, 9). Radius of the circle is 5√2 cm. (2023)
Ans: Given centre of a circle is(2a, a  7 )
Radius of the circle is 5√2 cm.
∴ Distance between centre (2a, a  7) and (11,  9 ) = radius of circle.
Q10: In what ratio, does xaxis divide the line segment joining the points A(3, 6) and B(12, 3) ? (2023)
(a) 1 : 2
(b) 1 : 4
(c) 4 : 1
(d) 2 : 1
Ans: (d)
Let the point on the xaxis be (x, 0) which divides the line segment joining the points A(3, 6) and B(12, 3) in the ratio k : 1
Using section formula, we have
Hence, the required ratio is 2 : 1.
Q11: Case Study: Jagdish has a Field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. (2023)
Based on the above information, answer the following questions:
(i) Taking O as origin, coordinates of P are (200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S?
(ii) (a) What is the area of square PQRS?
(b) What is the length of diagonal PR in square PQRS?
(iii) If S divides CA in the ratio K: 1, what is the value of K, where point A is (200, 800)?
Ans: (i) We have. P = (200, 0) and Q = (200, 0)
The coordinates of R and S are (200, 400) and (200, 400).
(ii) (a) The length PQ = 200 + 200 = 400 units.
Area of square PQRS = 400 x 400 = 160000 sq. units.
(b) Length of diagonal PR = √2 length of side = 400√2 units.
(iii) Here,
Using section formula, we have
Ans: (a)
Given, the equation of line is 4x 3y = 9.
Putting x = 0, we get 4 x 0  3y = 9 ⇒ y = 3
So, the line 4x  3y = 9 intersects the yaxis at (0, 3).
Q13: The point on xaxis equidistant from the points P(5, 0) and Q(1, 0) is (2022)
(a) (2, 0)
(b) (2, 0)
(c) (3, 0)
(d) (2, 2)
Ans: (a)
Let coordinates of the point on the xaxis be R (x, 0).
Given, PR = QR
⇒ PR^{2} = QR^{2}
⇒ (x  5)^{2} + (0  0)^{2} = (x + 1)^{2} + (0  0)^{2}
⇒ x^{2 } 10x + 25 = x^{2} + 2x + 1
⇒ 12x =24
⇒ x = 2
Required point is (2, 0).
Q14: The xcoordinate of a point P is twice its ycoordinate. If P is equidistant front Q(2, 5) and R(3, 6), then the coordinates of P are (2022)
(a) (8, 16)
(b) (10, 20)
(c) (20, 10)
(d) (16, 8)
Ans: (d)
Let coordinate of point P= t
So, .(xcoordinate of point P = 2t ∴ Point is P (2t, t).
Given, PQ = RP ⇒ PQ^{2} = RP^{2}
⇒ (2t  2)^{2} + (t + 5)^{2} = (2t + 3)^{2} + (t  6)^{2 }[By distance formula]
⇒ 4t^{2 } 8t + 4 + t^{2} + 10t + 25 = 4t^{2}+ 12t + 9 + t^{2} 12t + 36
⇒ 2t = 16
t = 8
Coordinates of P are (16, 8).
Q15: The ratio in which the point (4, 6) divides the line segment joining the points A(6, 10) and B(3, 8) is (2022)
(a) 2 : 5
(b) 7 : 2
(c) 2 : 7
(d) 5 : 2
Ans: (c)
Let point P(4, 6) divides the line segment AB in the ratio m_{1}: m_{2}.
By section formula, we have
Hence, required ratio is 2:7.
Q16: Case Study: Shivani is an interior decorator. To design her own living room, she designed wail shelves. The graph of intersecting wail shelves is given below: (2022)
Based on the above information, answer the following questions:
(i) If O is the origin, then what are the coordinates of S?
(a) (6, 4)
(b) (6, 4)
(c) (6, 4)
(d) (6, 4)
Ans: (c)
Coordinates of S are (6, 4).
(ii) The coordinates of the midpoint of the line segment joining D and H is
(a)
(b) (3, 1)
(c) (3, 1)
(d)
Ans: (b)
Coordinates of D are (2, 4) and coordinates of H are (8, 2).
∴ Midpoint of DH =
(iii) The ratio in which the xaxis divides the linesegment joining the points A and C is
(a) 2 : 3
(b) 2 : 1
(c) 1 : 2
(d) 1 : 1
Ans: (d)
Coordinates of A are (2, 4) and coordinates of C are (4, 4).
Let (x, 0) divides the line segment joining the points A and C in the ratio m_{1} : m_{2}
By section formula, we have
(iv) The distance between the points P and G is
(a) 16 units
(b) 3√74 units
(c) 2√74 units
(d) √74 units
Ans: (c)
Coordinates of P are (6, 4) and coordinates of G are (8, 6).
(v) The coordinates of the vertices of rectangle IJKL are
(a) I(2, 0), J(2, 6), K(8,6), L(8, 2)
(b) I(2, 2), J(2, 6), K(8,  6), L(8, 2)
(c) I(2, 0), J(2, 6), K(8, 6), L(8, 2)
(d) I(2, 0), J(2, 6), K(8, 6), L(8, 2)
Ans: (b)
Coordinates of vertices of rectangle IJKL are respectively I(2, 2), J(2, 6), K(8, 6),L(8, 2).
Q17: Case Study : Students of a school are standing in rows and columns in their school playground to celebrate their annual sports day. A, B, C and D are the positions of four students as shown in the figure. (2021)
Based on the above, answer the following questions:
(i) The figure formed by the four points A, B, C and D is a
(a) square
(b) parallelogram  v
(c) rhombus
(d) quadrilateral
Ans: (d)
From figure coordinates are A(2, 5), B(5, 7), C(8, 6) and D(6, 3)
Now,
Clearly, ABCD is a quadrilateral
(ii) If the sports teacher is sitting at the origin, then which of the four students is closest to him?
(a) A
(b) B
(c) C
(d) D
Ans: (a)
Here, sports teacher is at O(0,0).
Now,
∴ OA is the minimum distance
∴ A is closest to sports teacher.
(iii) The distance between A and C is
(a) √37 units
(b) √35 units
(c) 6 units
(d) 5 units
Ans: (a)
Required distance =
=
(iv) The coordinates of the mid point of line segment AC are
(a)
(b)
(c)
(d) (5, 11)
Ans: (c)
Coordinates of midpoint of AC are
(v) If a point P divides the line segment A D in the ratio 1: 2, then coordinates of P are
(a)
(b)
(c)
(d)
Ans: (b)
Let point P(x, y) divides the line segment AD in the ration 1: 2.
∴ Coordinates of P are
Q18: The distance between the points <m, n) and (m, n) is (2020)
(a)
(b) m + n
(c)
(d)
Ans: (c)
Required distance
Q19: The distance between t he points (0, 0) and (a  b, a + b) is (2020)
(a)
(b)
(c)
(d)
Ans: (d)
Required distance =
Q20: AOBC is a rectangle whose three vertices are A[0, 3), O(0, 0) and B(4, 0). The length of its diagonal is ______. (2020)
Ans: In rectangle AOBC. AB is a diagonal.
So,
= 5 Units
Q21: Show that the points (7, 10), (2, 5) and (3, 4) are vertices of an isosceles right triangle. (2020)
Ans: Let the given points be A(7, 10), B(2, 5) and C(3,  4].
Using distance Formula, we have
Since. AB = BC ∴ ABC is an isosceles triangle.
Also, AB^{2} + BC^{2} = 106 + 106 = 212 = AC^{2}
So. ABC is an isosceles right angled triangle with ∠B = 90°.
Q22: The point on the xaxis which is equidistant from (4, 0) and (10, 0) is (2020)
(a) (7, 0)
(b) (5, 0)
(c) (0, 0)
(d) (3, 0)
Ans: (d)
Let coordinates of the point on the xaxis be P(x, 0). Let the given points be A(4, 0) and B(10, 0). which also lie on xaxis.
Since P is equidistant from A and B.
∴ x = 4 + 10 / 2 = 6 / 2 = 3
So, P(3, 0) is equidistant from A(4, 0) and B(10, 0).
Q23: If the point P(k, 0) divides the line segment joining the points A(2, 2) and B(7, 4) in the ratio 1:2 then the value of k is (2020)
(a) 1
(b) 2
(c) 2
(d) 1
Ans: (d)
Since, the point P(k 0) divides the line segment joining A(2, 2) and B(7, 4) in the ratio 1 : 2.
Q24: The centre of a circle whose end points of a diameter are (6, 3) and (6, 4) is (2020)
(a) (8, 1)
(b) (4, 7)
(c)
(d)
Ans: (c)
Let the coordinates of centre of the circle be (x, y) and AB be the given diameter.
By Using midpoint formula.
We have,
∴ Coordinates of C are
Q25: Find the ratio in which the yaxis divides the line segment joining the points (6, 4) and (2, 7). Also, find the point of intersection. (2020)
Ans: Let the point P(0, y) on yaxis divides the line segment joining the points A(6, 4) and B(2, 7) in the ratio k : 1.
By section formula, we have
Hence, the required point is and required ratio is 3 : 1.
Q26: If the point C(1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B. (2020)
Ans: We have, A(2, 5), B(x, y) and C(1, 2) and point C divides AB in the ratio 3 :4.
∴ Coordinates of B = (5, 2)
Ans: Given AB = 5 units
Q28: Find the point on yaxis which is equidistant from the points (5,2) and (3, 2). (Delhi 2019)
Ans: Let P(0, y) be the point on the yaxis which is equidistant from A(5,  2) and B(3, 2).
AP = BP ⇒ (AP)^{2 }= (BP)^{2}
⇒ (5  0)^{2} + (2  y)^{2} = (3  0)^{2 }+ (2  y)^{2}
⇒ 25 + 4 + y^{2} + 4y = 9 + 4 + y^{2}  4y
⇒ 8y = 9  25
⇒ y = 16/2 = 2
Hence, A and B are equidistant from (0, 2).
Q29: Find the coordinates of a point A where AB is a diameter of the circle with centre (2, 2) and B is the point with coordinates (3, 4). (2019)
Ans: Let coordinates of the point A be (x, y) and O is the mid point of AB.
By using midpoint formula,
we have
⇒ 4 = x + 3 and4 = y + 4
⇒ x = 7 and y = 0
∴ Coordinates of A are (7, 0).
Q30: In what ratio is the line segment joining the points P(3, 6) and Q(5, 3) divided by xaxis? (2019)
Ans: Let the point R(x, 0) on xaxis divides the line segment PQ in the ratio k: 1.
∴ By section formula, we have
∴ Required ratio is 2 : 1 .
Q31: Find the ratio in which the segment joining the points (1, 3) sod (4, 5) is divided by xaxis? Also find the coordinates of this point on xaxis. (2019)
Ans: Let the point P(x, 0) divides the segment joining the points A(1, 3) and B (4, 5) in the ratio k : 1
Coordinates of P are [By Section Formula]
Since, ycoordinate of P is 0
.
Hence, the point P divides the line segment in the ratio 3 : 5.
Also, xcoordinate of P
=
∴ Coordinates of point P are (17/8, 0)
Q32: The point R divides the line segment AB, where A ( 4, 0) and B(0, 6) such that AR = 3/4 AB.
Find the coordinates of R. (2019)
Ans: Given,
∴ Coordinates of R are
Q33: Find the coordinates of a point A. where AB is a diameter of the circle with centre (3, 1) and the point B is (2, 6). [2019, 2 Marks]
Ans: Let the coordinates of A be (x, y). Here, 0(3,  1] is the mid point of AB.
By using mid point formula, we have⇒ x = 4, y =  8∴ Coordinates of A are (4,  8).
Q34: The line segment joining the points A(2, 1) and B(5, 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the fine given by 2x  y + k = 0, find the value of k. (2019)
Ans:
Let P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) are the points of trisection of line segment AB.
∴ AP = PQ = QB
Now. point P divides AB internally in the ratio 1 : 2
∴ By section formula, we have
Since, point P(3, 2) lies on the line 2x  y + k = 0
⇒ 6 + 2 + k = 0
⇒ k =  8
Q35: Find the ratio in which the line x  3y = 0 divides the line segment joining the points (2, 5) and (6, 3). Find the coordinates of the point of intersection. (2019)
Ans: Let point P(x_{1}, y_{1}) divides the line segment joining the points A(2, 5) and B(6, 3) in the ratio k: 1
∴ Coordinates of P are
The point P lies on line x  3y = 0
∴ Required ratio is 13 : 3.Now, coordinates of P are
Q36: In what ratio does the point P(4, y) divide the line segment joining the points A(6, 10) and B(3, 8) Hence find the value of y. (2019)
Ans: Let the point P(4, y) divides the line segment joining the points A and B in the ration k: 1
∴ By section formula, coordinates of P are
∴ Required ration is 2: 7.
Now,
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