Maths : Coordinate Geometry: Book Back, Exercise, Example Numerical Question with Answers, Solution: Exercise 5.6: Multiple Choice Questions, One Mark Choose the correct Answers

**Coordinate Geometry**

**Exercise 5.6**

**Multiple Choice Questions**

1. If the
y-coordinate of a point is zero, then the point always lies ______

(1) in the
I quadrant

(2) in the
II quadrant

**(3) on x-axis **

(4) on y-axis

**Solution:**

Points in *x* - axis has *y* - coordinate zero

**[Answer: (3) on x-axis]**

2. The points
(–5, 2) and (2, –5) lie in the ________

(1) same
quadrant

(2) II and
III quadrant respectively

**(3) II and IV quadrant respectively **

(4) IV and
II quadrant respectively

**Solution:**

(–, +) lies II^{nd}
quadrant and (+,–) lies in IV^{th}
quadrant** **

**[Answer: (3) II and IV quadrant respectively]**

3. On plotting
the points *O*(0,0), *A*(3, – 4), *B*(3, 4) and *C*(0, 4) and
joining *OA, AB, BC* and *CO*, which of the following figure is obtained?

(1)
Square

(2)
Rectangle

**(3) Trapezium **

(4)
Rhombus

**Solution:**

In trapezium one pair of opposite side is parallel.

**[Answer: (3) Trapezium]**

4. If
*P*( –1,1), *Q*( 3,–4), *R*( 1, –1), *S*(–2, –3) and *T*(
–4, 4) are plotted on a graph paper, then the points in the fourth quadrant are
__________

(1) *P *and* T*

**(2)
Q and R**

(3) only *S*

(4) *P* and *Q*

**Solution:**

Points in IV^{th} quadrant are (+,–)

**[Answer: (2) Q and R]**

5. The
point whose ordinate is 4 and which lies on the *y*-axis is _______________

(1)( 4, 0 )

**(2) (0, 4)**** **

(3) (1, 4)

(4) (4, 2)

**Solution:**

Points in *y*-axis have abscissa *a* zero

**[Answer: (2) (0, 4)]**

6. The
distance between the two points ( 2, 3 ) and ( 1, 4 ) is ______

(1)
2

(2)
√56

(3)
√10

**(4) √2**

**Solution:**

Distance = √[(*x*_{2}–*x*_{1})^{2}+(*y*_{2}–*y*_{1})^{2}]

**[Answer: (4) √2]**

7. If
the points *A* (2,0), *B* (-6,0), *C* (3, *a*–3) lie on the
*x*-axis then the value of *a* is _____

(1) 0

(2) 2

**(3) 3****
**

(4) –6

**Solution:**

Points in *y*-axis have ordinate
zero.

*a*–3 = 0

⇒ a = 3

**[Answer: (3) 3]**

8. If ( *x*+2,
4) = (5, *y–*2), then the coordinates (*x,y*) are _____

(1) (7, 12)

(2) (6, 3)

**(3) (3, 6) **

(4) (2, 1)

**Solution:**

* x* + 2 = 5 ⇒ *x* = 3; *y* *–* 2 = 4 ⇒ *y* = 6

**[Answer: (3) (3, 6)]**

9. If Q_{1},
Q_{2}, Q_{3}, Q_{4} are the quadrants in a Cartesian plane
then Q_{2} ∩ Q_{3} is ___________

(1) Q_{1}∩ Q_{2}

(2) Q_{2}∩Q_{3}

**(3) Null set **

(4) Negative
x-axis.

**Solution:**

Quadrants do not contain the axis.

**[Answer: (3) Null set]**

10. The distance
between the point ( 5, –1 ) and the origin is _________

(1) √24

(2) √37

**(3) √26 **

(4) √17

**Solution:**

Distance = √[(5-0)^{2} + (–1 – 0)^{2}] = √[5^{2}+l^{2}]
= √26

**[Answer: (3) √26]**

11. The coordinates
of the point C dividing the line segment joining the points P(2,4) and Q(5,7) internally
in the ratio 2:1 is

(1) (7/2,
11/2)

(2) (3,5)

(3) (4,4)

**(4) (4,6) **

**Solution:**

**[Answer: (4) (4,6)]**

12. If P
(*a*/3,*b*/2) is the mid-point of the line segment joining A(−4,3) and B(−2,4)
then (*a,b*) is

**(1) (−9,7) **

(2) (−3,
7/2)

(3) (9, −7)

(4) ( 3,
−7/2 )

**Solution:**

**[Answer: (1) (−9,7)]**

13.
In what ratio does the point *Q*(1,6) divide the line segment joining the points
*P*(2,7) and *R*(−2,3)

(1) 1:2

(2) 2:1

**(3) 1:3**** **

(4) 3:1

**Solution:**

**[Answer: (3) 1:3]**

14.
If the coordinates of one end of a diameter of a circle is (3,4) and the coordinates
of its centre is (−3,2), then the coordinate of the other end of the diameter is

(1) (0,−3)

(2) (0,9)

(3) (3,0)

**(4) (−9,0)**

**Solution:**

**[Answer: (4) (−9,0)]**

15.
The ratio in which the *x*-axis divides the line segment joining the points
*A*(*a*_{1} ,*b*_{1} ) and *B *(*a*_{2}*
*,*b*_{2}* *)* *is

(1) *b*_{1}
: *b*_{2}

**(2) ****−***b*_{1}** : b_{2}**

(3) *a*_{1}
: *a*_{2}

(4) −*a*_{1} : *a*_{2}

**Solution:**

**[Answer: (2) ****−***b*_{1}** : b_{2}]**

16.
The ratio in which the *x*-axis divides the line segment joining the points
(6,4) and (1, −7) is

(1) 2:3

(2) 3:4

**(3) 4:7**** **

(4) 4:3

**Solution:**

**[Answer: (3) 4:7]**

17.
If the coordinates of the mid-points of the sides *AB*, *BC* and *CA*
of a triangle are (3,4), (1,1) and (2,−3) respectively, then the vertices *A*
and *B* of the triangle are

(1) (3,2), (2,4)

**(2) (4,0), (2,8)**** **

(3) (3,4), (2,0)

(4) (4,3), (2,4)

**Solution:**

**[Answer: (2) (4,0), (2,8)]**

18.
The mid-point of the line joining (−*a*,2*b*) and (−3*a*,−4*b*)
is

(1) (2*a*,3*b*)

**(2) (−2 a, −b)**

(3) (2*a*,*b*)

(4) (−2*a*, −3*b*)

**Solution:**

**[Answer: (2) (−2 a, −b)]**

19.
In what ratio does the *y*-axis divides the line joining the points (−5,1)
and (2,3) internally

(1) 1:3

(2) 2:5

(3) 3:1

**(4) 5:2**

**Solution:**

**[Answer: (4) 5:2]**

20.
If (1,−2), (3,6), (*x*,10) and (3,2) are the vertices of the parallelogram
taken in order, then the value of *x* is

(1) 6

**(2) 5****
**

(3) 4

(4) 3

**Solution:**

In parallelogram diagonals
bisect each other.

Mid point of AC = Mid
point of BD

6− (−2) / 3−1 = 10−2 / *x*−3

8/2 = 8/*x*−3

*x*−3 = 2

* x *= 5

**[Answer: (2) 5]**

Tags : Numerical Problems with Answers, Solution | Coordinate Geometry | Maths , 9th Maths : UNIT 5 : Coordinate Geometry

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9th Maths : UNIT 5 : Coordinate Geometry : Exercise 5.6: Multiple Choice Questions | Numerical Problems with Answers, Solution | Coordinate Geometry | Maths

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