# MCQs for NCERT Class 9 Mathematics Chapter 3 Coordinate Geometry

Please refer to the MCQ Questions for Class 9 Mathematics Chapter 3 Coordinate Geometry with Answers. The following Coordinate Geometry Class 9 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 9. Our experts have designed MCQ Questions for Class 9 Mathematics with Answers for all chapters in your NCERT Class 9 Mathematics book.

## Coordinate Geometry Class 9 MCQ Questions with Answers

See below Coordinate Geometry Class 9 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. Points (6, 8), (3, 7), (–2, –2) and (1, –1) are joined to form a quadrilateral. What will be the structure of quadrilateral?
(A) Rhombus
(B) Parallelogram
(C) Square
(D) Rectangle

Ans.

B

Question. Find the area (in square units) of the triangle whose vertices are (a, b + c), (a, b – c) and (–a, c).
(A) 2ac
(B) 2bc
(C) b(a + c)
(D) c(a – b)

Ans.

A

Question.. Find the area of the quadrilateral, the coordinates of whose angular points taken in order are (1, 1), (3, 4), (5, –2) and (4, –7).
(A) 20.5 sq. units
(B) 41 sq. units
(C) 82 sq. units
(D) 61.5 sq. units

Ans.

A

Question. Four vertices of a parallelogram taken in order are (–3, –1), (a, b), (3, 3) and (4, 3). What will be the ratio of a and b?
(A) 4 : 1
(B) 1 : 2
(C) 1 : 3
(D) 3 : 1

Ans.

A

Question. The points (1, 1), (–1, 5), (7, 9) and (9, 5) taken in such order that it will form a
(A) Rectangle
(B) Square
(C) Rhombus
(D) None of these

Ans.

A

Question. If the points (a, 0), (0, b) and (1, 1) are collinear then which of the following is true?
(A) 1/a + 1/b = 2
(B) 1/a – 1/b = 1
(C) 1/a – 1/b = 2
(D) 1/a + 1/b = 1

Ans.

D

Question. Three points A(1, –2), B(3, 4) and C(4, 7) form
(A) A straight line
(B) An equilateral triangle
(C) A right-angled triangle
(D) None of these

Ans.

A

Question. The coordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2). What will be the coordinates of the centroid of the triangle?

Ans.

A

Question. Area of quadrilateral formed by the vertices (–1, 6), (–3, –9), (5, –8) and (3, 9) is _______ (sq. units).
(A) 96
(B) 18
(C) 50
(D) 25

Ans.

A

Question. Find the area of triangle whose vertices are (t, t – 2), (t + 2, t + 2) and (t + 3, t).
(A) 14 sq. units
(B) 2t sq. units
(C) 5 sq. units
(D) 4 sq. units

Ans.

D

Question. The vertices of a DABC are A(2,1), B(6, –2), C(8, 9). If AD is angle bisector, where D meets on BC, then coordinates of D are _______.
(A) (20/3, 5.3)
(B) (5, 2)
(C) (4, 3)
(D) (14, 3, 7/3)

Ans.

A

Question. The coordinates of the third vertex of an equilateral triangle whose two vertices are at (3, 4), (–2, 3) are ________.
(A) (1, 7)
(B) (5, 1)
(C) (1+√3/2, 7-5√3/2) or (1-√3/2, 7 + 5√3/2)
(D) (-5, 5)

Ans.

C

Question. In what ratio is the line segment joining the points (–3, 2) and (6, 1) is divided by Y-axis ?
(A) 1 : 3
(B) 2 : 1
(C) 1 : 2
(D) 3 : 1

Ans.

C

Question. Find the coordinates of the point on X-axis which are equidistant from the points (–3, 4) and (2, 5).
(A) (20, 0)
(B) (–23, 0)
(C) (4/7X0)
(D) None of these

Ans.

D

Question. If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
(A) abc
(B) 0
(C) a + b + c
(D) 3 abc

Ans.

D

Question. Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines)
(A) 2.2 km
(B) 2.7 km
(C) 11 √3km
(D) 2.40 km

Ans.

D

DIRECTION (17-18) : Students of a school are standing in rows and columns in their playground for drill practice. A, B, C and D are the position of the four students as shown in the figure.

Question. What is the difference of distance between AC and AD ?
(A) 2 units
(B) 2.14 units
(C) 8 units
(D) 2.3 units

Ans.

D

Question.. If Mohit wants to stand in such a way that he is equidistance from each of the four students A, B, C and D then what are the coordinate of his position ?
(A) (6, 6)
(B) (7, 5)
(C) (6, 4)
(D) (4, 6)

Ans.

B

Question. A well planned locality, has two straight roads perpendicular to each other. There are 5 lanes parallel to Road – I. Each lane has 8 houses as seen in figure. Chaitanya lives in the 6th house of the 5th lane and Hamida lives in the 2nd house of the 2nd lane. What will be the shortest distance between their houses?

(A) 10 units
(B) 12 units
(C) 6 units
(D) 5 units

Ans.

A

Question. To raise social awareness about the hazards of smoking, a school decided to start “No smoking campaign”. A student is asked to prepare a campaign banner in the shape of a triangle shown in the figure. If cost of 1 cm2 of banner is ₹ 2, find the cost of the banner.

(A) `12 `
`(B)`6
(C) `5 `
`(D)`10

Ans.

D

Question. The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is ________.
(A) (2, 11)
(B) (11, 2)
(C) (11, – 2)
(D) (– 2, 11)

Ans.

A

Question. If A(2, 2), B(4, 4) and C(2, 6) are the vertices of a triangle ABC and D, E and F are the mid point of AB, BC and AC respectively, then
(i) Find the area of ΔABC.
(ii) Find the area of ΔDEF.
(iii) Find the ratio of area of ΔDEF to ΔABC.
(i)             (ii)          (iii)
(A) 8 sq. units 2 sq. units    1 : 4
(B) 6 sq. units 3 sq. units    1 : 2
(C) 4 sq. units 1 sq. units    1 : 4
(D) 3 sq. units 1 sq. units    1 : 3

Ans.

C

Question. The values of t, if the area of the pentagon ABCDE be 45 / 2 sq. units where A = (1, 3), B = (–2, 5), C = (–3, –1), D = (0, –2) and E = (2, t) are ________.
(A) –1, 17
(B) –1, 106
(C) 1, 17
(D) 1, 18

Ans.

A

Question. If (–2, 1), (a, 0), (4, b) and (1, 2) are the vertices of a parallelogram, then
(i) Find a
(ii) Find b
(iii) Area of the parallelogram.
(i)     (ii)        (iii)
(A) 1 –1     10 sq.   units
(B) 1 –2     6 sq.     units
(C) 1 1       6 sq.     units
(D) –1 –1   6 sq.     units

Ans.

C

Question. In the given figure, PQRS is a straight line R is the mid point of QS and Q is the mid point of PS. S is (6, 5), R is (3, 5) and T is (4, 8). Find the length of median TU.
(A) √13 units
(B) √50 units
(C) 2 √28 units
(D) √58 units

Ans.

D