$\text{ABCD}$ is a rectangle whose three vertices are $B(4, 0), C(4, 3)$ and $D(0, 3)$. The length of one of its diagonals is :
- ✓$5$
- B$4$
- C$3$
- D$25$
Answer: A.
View full solution →Question types
Coordinate Geometry question types
296 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
296
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
201 Q→02Assertion (A) & Reason (B) MCQ
28 Q→03True False[1 Marks ]
12 Q→04Fill In The Blanks[1 Marks ]
3 Q→051 Marks Question
7 Q→062 Marks Questions
17 Q→073 Marks Question
7 Q→085 Marks Questions
4 Q→09Case study (4 Marks)
17 Q→Sample Questions
Coordinate Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The distance of the point $(–3, 4)$ from the $x-$ axis is :
- A$3$
- B$-3$
- ✓$4$
- D$5$
Answer: C.
View full solution →In Figure $2, P(5, - 3)$ and $Q(3, y)$ are the points of trisection of the line segment joining $A(7, –2)$ and $B(l, –5)$. Then $y$ equals
- A$2$
- B$4$
- ✓$–4$
- D$-\frac{5}{2}$
Answer: C.
View full solution →If $\text{P}\Big(\frac{\text{a}}{2},4\Big )$ is the mid $-$ point of the line-segment joining the point $(-6, 5)$ and $B(- 2, 3),$ then the value of a is :
- ✓$-8$
- B$3$
- C$-4$
- D$4$
Answer: A.
View full solution →If the points $A(x, 2), B(-3, -4) $ and $C(7, -5)$ are collinear, then the value of $x$ is :
- ✓$-63$
- B$63$
- C$60$
- D$-60$
Answer: A.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as :
Assertion $(A)$ : The point $(0, 4)$ lies on $y-$ axis.
Reason $(R)$ : The $x-$ coordinate on the point on $y-$ axis is zero.
Assertion $(A)$ : The point $(0, 4)$ lies on $y-$ axis.
Reason $(R)$ : The $x-$ coordinate on the point on $y-$ axis is zero.
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Mid $-$ point of a line segment divides line in the ratio $1 : 1$.
Reason : If area of triangle is zero that means points are collinear.
Assertion : Mid $-$ point of a line segment divides line in the ratio $1 : 1$.
Reason : If area of triangle is zero that means points are collinear.
- A$A$ is true $,R$ is true; $R$ is a correct explanation for $A.$
- ✓$A$ is true $,R$ is true; $R$ is not a correct explanation for $A.$
- C$A$ is true; $R$ is False.
- D$A$ is false; $R$ is true.
Answer: B.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion : Three points $A, B, C$ are such that $AB + BC > AC,$ then they are collinear.
Reason : Three points are collinear if they lie on a straight line.
Assertion : Three points $A, B, C$ are such that $AB + BC > AC,$ then they are collinear.
Reason : Three points are collinear if they lie on a straight line.
- A$A$ is true $ ,R$ is true; $R$ is a correct explanation for $A.$
- B$A$ is true $,R$ is true; $R$ is not a correct explanation for $A$.
- C$A$ is true; $R$ is False.
- ✓$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : The point $(0, 4)$ lies on $y -$ axis.
Reason : The $x -$ coordinate on the point on $y -$ axis is zero.
Assertion : The point $(0, 4)$ lies on $y -$ axis.
Reason : The $x -$ coordinate on the point on $y -$ axis is zero.
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : Mid $-$ point of a line segment divides line in the ratio $1 : 1.$
Reason : The ratio in which the point $(-3, k)$ divides the line segment joining the points $(-5, 4)$ and $(-2, 3)$ is $1 : 2.$
Assertion : Mid $-$ point of a line segment divides line in the ratio $1 : 1.$
Reason : The ratio in which the point $(-3, k)$ divides the line segment joining the points $(-5, 4)$ and $(-2, 3)$ is $1 : 2.$
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: C.
View full solution →State whether the following statements are true or false. Justify your answer.
Points A(4, 3), B(6, 4), C(5, -6) and D(-3, 5) are the vertices of a parallelogram.
Points A(4, 3), B(6, 4), C(5, -6) and D(-3, 5) are the vertices of a parallelogram.
State whether the following statements are true or false. Justify your answer.
The points (0, 5), (0, -9) and (3, 6) are collinear.
The points (0, 5), (0, -9) and (3, 6) are collinear.
State whether the following statements are true or false. Justify your answer.
The points A(-1, -2), B(4, 3), C(2, 5) and D(-3, 0) in that order form a rectangle.
The points A(-1, -2), B(4, 3), C(2, 5) and D(-3, 0) in that order form a rectangle.
State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
State whether the following statements are true or false. Justify your answer.
$\triangle\text{ABC}$ with vertices A(-2, 0), B(2, 0) and C(0, 2) is similar to $\triangle\text{DEF}$ with vertices D(-4, 0) and F(0, 4).
View full solution →$\triangle\text{ABC}$ with vertices A(-2, 0), B(2, 0) and C(0, 2) is similar to $\triangle\text{DEF}$ with vertices D(-4, 0) and F(0, 4).
AOBC is a rectangle whose three vertices are A(0, – 3), O(0, 0) and B(4, 0). The length of its diagonal is ________.
The distance between the points (a, b) and (-a, -b) is _________.
The distance between the points $\Big(-\frac{8}{5},2\Big)$ and $\Big(\frac{2}{5},2\Big)$is _________.
View full solution →Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.
Find the distance between the pair of points (a, b), (-a, -b)
Find the distance between the pair of points (-5, 7), (-1, 3)
Find the distance between the pair of points: (2, 3), (4, 1)
If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = $\frac{3}{7}$ AB and P lies on the line segment AB.
View full solution →Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4).$
View full solution →If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Find the ratio in which the segment joining A(1, -5) and B(-4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Find the area of the rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.
[Hint: Area of a rhombus $=\frac{1}{2}$ (product of its diagonals)]
View full solution →[Hint: Area of a rhombus $=\frac{1}{2}$ (product of its diagonals)]
Find the point on the x-axis which is equidistant from $(2, -5)$ and $(-2, 9).$
View full solution →Name the type of quadrilateral formed, if any, by the points (4, 5), (7, 6), (4, 3), (1, 2), and give a reason for your answer.
Name the type of quadrilateral formed, if any, by the points $(-3, 5), (3, 1), (0, 3), (-1, -4)$, and give a reason for your answer.
View full solution →Name the type of quadrilateral formed, if any, by the points (-1, -2), (1, 0), (-1, 2), (-3, 0), and give a reason for your answer.
Show that the points A (1, 7), B (4, 2), C (-1, -1) and D (-4, 4) are the vertices of a square.
Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
To conduct Sports Day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Figure. Niharika runs $\frac{1}{4}$th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
View full solution →Find the coordinates of the points of trisection of the line segment joining $(4, –1)$ and $(–2, –3).$
View full solution →In a classroom, 4 friends are seated at the four points A, B, C and D as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, Don’t you think ABCD is a square? Chameli disagrees. Using distance formula, find which of them is correct.
Ravish was wishing to buy a new car but he didnt had enough of money. One of his friend suggested him to take a loan from XYZ bank. Influenced by his idea, he decides to take a loan of Rs. 1,18,000 and decides to repay by Rs. 1000 per month. On a further note, he decides to increasethe installment by Rs. 100 every month. Answer the following questions.
(i) What is the amount paid by him in 30th installment?
(ii)What is the total amount paid by him in 30 installments?
OR
What is the ratio of first and last installment?
(iii) If the total number of installments is 40, what is the amount paid in the last installment?3
(i) What is the amount paid by him in 30th installment?
(ii)What is the total amount paid by him in 30 installments?
OR
What is the ratio of first and last installment?
(iii) If the total number of installments is 40, what is the amount paid in the last installment?3
There are two routes to travel from source A to destination B by bus. First bus reaches at B via point C and second bus reaches from A to B directly. The position of A, B and C are represented in the following graph:
Based on the above information, answer the following questions.
(1) The distance between A and B is
(ii) The distance between A and C is
(iii) If the fare for first bus is 10/km, then what will be the fare for total journey by that bus?
OR
If the fare for second bus is 15/km, then what will be the fare to reach to the destination by
this bus?
Amit was playing a number card game. In the game, some number cards (having both +ve or-ve
numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6th and 14th card and finds their sum to be -76. On the second turn he picks up 8th and 16th card and finds their sum to be -96.ased on the above information, answer the following questions.
(i) What is the difference between the numbers on any two consecutive cards?
(ii) The number on first card is,
(iii) What is the number on the 19th card?
OR
What is the number on the 23rd card?
numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6th and 14th card and finds their sum to be -76. On the second turn he picks up 8th and 16th card and finds their sum to be -96.ased on the above information, answer the following questions.
(i) What is the difference between the numbers on any two consecutive cards?
(ii) The number on first card is,
(iii) What is the number on the 19th card?
OR
What is the number on the 23rd card?
During the covid period, everyone started using his/her savings. Gauri and Sheetal also used her
savings which they both saved in the past few years. Here is the saving pattern of both of the girls for the last 15 weeks. Gauri saved in a pattern of Rs. 10 in first week, Rs. 12 in second week, Rs.14 in third week and so on while Sheetal saved Rs. 10 in first week, Rs. 13 in second week, Rs.16 in third week and so on.
(i)What is the amount saved by Gauri after 15 weeks?
(ii) What is the difference in total saving of Gauri and Sheetal 10th week?
OR
What is the difference in saving of Gauri and Sheetal at the end of 15 weeks?
(iii) Who saved more?
The diagram shows the plans for an area outside the city. The area is going to be built and
constructed to expand the main city's domain. The land is to be used carefully with a proper
planning and executions. A map as shown in the above figure is sketched to be built. It has
educational premises near the housing area. Also, a library and a skate park are planned for the
extra activities and refreshments for the people of the city. Refer to the information and image,imagining the outer area as a cartesian plane. (Distances measured are in units)
(i)How far apart is the school from home
(ii) Find the area for the figure formed from joining line segments between home, school and
library.
OR
Find the area for the figure formed from joining
line segments between skate park, school and library.
(iii) Locate the position of home from skate park.
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