Aptitude - Co-ordinate Geometry Online Quiz


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Following quiz provides Multiple Choice Questions (MCQs) related to Co-ordinate Geometry. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Questions and Answers

Q 1 - In which quadrant does the point (2, 5) lies?

A - First

B - second

C - third

D - fourth

Answer : A

Explanation

The Point (2, 5) lies in 1st quadrant

Q 2 - The separation between the point A (b, 0) and B (0, a) is:

A - √ a2-b2

B - √a2+b2

C - √a+b

D - (a+b)

Answer : B

Explanation

AB =   √ (b-0)2+ (0-a) 2   = √ b2+a2 = √a2+b2

Q 3 - The focuses A (0,6),B(- 5,3) and C(3,1) are the vertices of a triangle which is:

A - Isosceles

B - equilateral

C - scalene

D - right calculated

Answer : A

Explanation

AB2= (-5-0) 2+ (3-6) 2= (-5) 2+ (-3) 2= (25+9) = 34
BC2= (3+5) 2+ (1-3) 2= (8) 2+ (-2) 2= 64+4 = 68
AC2= (3-0) 2+ (1-6) 2= (3) 2+ (-5) 2= 9+25 = 34
∴ AB= AC. Hence, ∆ABC is isosceles.

Q 4 - The focuses A (1,2) ,B(5,4) ,C(3,8) and D(- 1,6) taken all together are the vertices of

A - A rectangle

B - a rhombus

C - a square

D - none of these

Answer : C

Explanation

vertices
AB2= (5-1) 2+ (4-2) 2= (16+4) = 20
BC2= (3-5) 2+ (8-4) 2= (4+16) = 20
CD2= (-1-3) 2+ (6-8) 2= (16+4) = 20
DA2= (1+1) 2+ (2-6) 2= (4+16)=20
∴ AB= BC= CD= DA= √20
Diagonal AC2= (3-1) 2+ (8-2) 2= (4+36) = 40
Diagonal BD2= (-1-5) 2+ (6-4) 2= (36+4) = 40
∴ Diag AC= Diag BD =√40
∴ ABCD is a square.

Q 5 - The end purposes of the distance across of a circle are A (4,- 1) and B(- 2,- 5). The co-ordinates of its middle are:

A - (1, - 3)

B - (2, - 4)

C - (- 1, 2)

D - (- 2, 3)

Answer : A

Explanation

Co-ordinates of the center are [4+ (-2)/2, -1+ (-5)/2], i.e. (1,-3)

Q 6 - In what proportion does the point P (2, - 5) separate the line fragment joining A (- 3, 5) and B (4, - 9)?

A - 2:3

B - 4:3

C - 5:1

D - 5:2

Answer : D

Explanation

Let the required ratio be ℏ:1
 Then, the point P is [(4ℏ-3/ℏ+1), (-9ℏ+5/ℏ+1)]
 ∴ 4ℏ-3/ℏ+1 =2,-9ℏ+5/ℏ+1=-5
 ⇒ 4ℏ-3= 2ℏ+2 and -9ℏ+5 = -5ℏ-5
 ⇒ 2ℏ= 5 and 4ℏ=10 ⇒ ℏ= 5/2
 Required ratio is 5/2:1, i.e. 5:2

Q 7 - In what proportion is the line portion joining the focuses A (6, 3) and B (- 2, - 5) partitioned by the x-hub?

A - 3:2

B - 3:5

C - 1:2

D - 2:5

Answer : C

Explanation

  Let x-axis cut the join of A (6, 3) and B (-2,-5) in the ratio ℏ:1 at the point.
 Then, co-ordinates of P are P [(-2ℏ+6/ℏ+1), (-5ℏ+3/ℏ+1)
 But, P lies on x-axis. So, its ordinate is 0. 
 ∴ -5ℏ+3/ℏ+1 =0 ⇒ -5ℏ+3 =0 ⇒ ℏ= 3/5
 Required ratio is 3/5:1 i.e., 1:2.

Q 8 - A line goes through the focuses A (- 2, 3) and B (- 6, 5). The slop of line AB is

A - - 1/2

B - 1/2

C - 3/4

D - -1

Answer : A

Explanation

  Slop = (y₁ ?y₂)/( x₁-x₂) = (5-3)/(-6+2) = 2/-4 =-1/2

Q 9 - On the off chance that the slop of a line going through the focuses A (2, 5) and B(x, 3) is 2, then x=?

A - 1

B - 2

C - -1

D - -2

Answer : A

Explanation

   (3-5)/x-2 =2 ⇒ 2x-4 =-2 ⇒ 2x =2 ⇒ x= 1

Q 10 - The mathematical statement of a line passing through (3, 4) and parallel to x-pivot is:

A - y-4 =0

B - y-1 =0

C - y+4 = 0

D - none of these

Answer : C

Explanation

The equation of the line is y+4/x-3 = tan0= 0 ⇒ y+4 = 0


aptitude_coordinate_geometry.htm

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