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Aptitude - Co-ordinate Geometry Online Quiz

Quiz

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.

Q 1 - In which quadrant does the point (- 3, - 5) lies?

Answer : C

Explanation

The point (-3,-5) lies in 3rd quadrant

Q 2 - The separation of the point A (7, 4) and B (0, a) is:

Answer : D

Explanation

AB² = (7-3)²+ (4-1)² = (4²+3²) = (16+9) =25 ⇒ AB= √25 = 5 unit.

Q 3 - The separation of the point A (2, - 3) and B (2, 2) is:

Answer : D

Explanation

AB²= (2-2) ²+ (-3-2) ²= 0+25=25 ⇒ AB =√ 25 =5 unit

Q 4 - The focuses A (1,- 3) ,B(13,9) ,C(10,12) and D(- 2,0) taken all together are the vertices of :

Answer : A

Explanation


AB²= (13-1) ²+ (9+3) ²= (144+144) = 288.
BC²= (10-13) ²+ (12-9) ²= (9+9) = 18
CD²= ((10+2) ²+ (12-0) ²= (144+144) = 288
AD²= (-2-1) ²+ (0+3) ²= (9+9) = 18
∴ ab= cd and BC= AD
Diag AC²= (10-1) ²+ (12+3) ²= (81+225) = 306
Diag BD²= (-2-13) ²+ (0-9) ²= (225+81) = 306
∴Diag AC= Diag BD
∴ ABCD is a rectangle.

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

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 - A point C partitions the join Of A (1, 3) and B (2, 7) in the proportion 3:4. The co-ordinates of C are:

Answer : C

Explanation

Co-ordinates of C are [(5*2+4*1/3+4), (3*7+4*3/ 3+4) i.e. (10/7, 33/7)

Q 7 - y-pivot partitions the join of P (- 4, 2) and Q (8, 3) in the proportion

Answer : D

Explanation

Let the required ratio be ℏ:1. Then, its co-ordinates are [(8ℏ -4 / ℏ +1, 3ℏ +2/ℏ +1)]
 But lies on y-axis. So, its abscissa is 0.
 ∴ 8ℏ  -4 / ℏ +1=0  ⇒ 8ℏ  -4  =0 ⇒ ℏ =1/2
Required ratio is 1/2:1, 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

Answer : A

Explanation

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

Q 9 - A line goes through the point (3, 5) and makes an edge of 135⁰with the x-pivot. The mathematical statement of the line is:

Answer : A

Explanation

The equation of the line is:
 Y-5/x-3 = tan 135⁰ = tan (180⁰-45⁰) = -tan 45⁰ =-1
 ⇒ Y-5 =3-x = > x+y -8 = 0

Q 10 - The estimation of ℏ for which the line x+2y-9= 0 and ℏx+4y+5 =0 are parallel, is

Answer : A

Explanation

Since the given lines are parallel, we have 1/ℏ =2/4 ⇒ ℏ = 2

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