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 (4, - 6) lies?

A - First

B - second

C - third

D - fourth

Answer : D

Explanation

The point (4,-6) lies in 4th quadrant

Q 2 - The separation of the point p (8, - 6) from the beginning is:

A - 2 units

B - 14 units

C - 10 units

D - none of these

Answer : C

Explanation

Op = √ (8-0)2+ (-6-0)2 = √64+ 36    = √100 =10 unit

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 - In the event that the focuses A(1,- 1) , B(5,2) and C(ℏ,5) are collinear , then ℏ=?

A - 6

B - -3

C - 0

D - 4

Answer : C

Explanation

Here x₁=1, x₂= 5, Xᴈ = ℏ, y₁ =-1, y₂= 2 and Yᴈ = 5
 ∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)]
  1. (2-5) +5(5+1) +ℏ (-1-2) = 0
  -3+30-3ℏ=0   3ℏ =27  ℏ =0

Q 6 - Two vertices of a ∆ ABC are B (- 3, 1) and C (0, - 2) and its centroid is at the inception. The Third vertex A is:

A - (3, 1)

B - (2, 3)

C - (- 1, 2)

D - (- 2, 3)

Answer : A

Explanation

  Let the vertex A be (a, b). Then,
 1/3 (-3+0+a) =0 and 1/3 (1-2+b) =0
 = -3 +a =0 and -1 +b=0 ⇒ a=3 and b= 1
 ∴ Vertex A is A (3, 1)

Q 7 - x-pivot partitions the join of A (2, 3) and B (5, 6) in the proportion

A - 1:2

B - 2:1

C - 3:5

D - 2:3

Answer : A

Explanation

Let the required ratio be ℏ:1. Then, its co- ordinates are (5ℏ+2/ ℏ+1, 6ℏ-3/ℏ+1)
 But, it lies on x-axis. So, its ordinate is 0.
 ∴ 6ℏ-3/ℏ+1 =0 ⇒ 6ℏ-3 =0 ⇒ ℏ=1/2
 Required ratio is 1/2:1 i.e., 1:2

Q 8 - The slop of a line going through the focuses A (4, 3) and B (6, 3) is:

A - 2

B - ∞

C - 0

D - none of these

Answer : C

Explanation

Slop = (y₁ ?y₂)/( x₁-x₂) = (-3+3)/(6-4) =0/2 =0

Q 9 - The slop of a line going through the focuses A (3, - 1) and B (3, 2) is:

A - 0

B - 3

C - not characterized

D - none of these

Answer : C

Explanation

Slop = (y₁ ?y₂)/( x₁-x₂) = (2+1)/ (3-3) = 3/0, which is not defined

Q 10 - The estimation of ℏ for which the line2 x+ℏy+7= 0 and 27x-18y+25=0 are opposite to one another, is

A - ℏ= - 1

B - ℏ= 2

C - ℏ= 3

D - ℏ = - 2

Answer : C

Explanation

2x+ℏY+7 =0 ⇒ ℏY =-2-7 ⇒ y = -2x/ℏ- 7/ℏ
 27x-18y +25 =0 ⇒ 18y = 27x+25 ⇒ y= 3x/2 +25/18
 ∴ -2/ℏ *3/2 = -1 ⇒ ℏ =3.


aptitude_coordinate_geometry.htm

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