Aptitude - Questions & Answers

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 (- 5, 7) lies?

Answer : B

Explanation

The point (-5, 7) lies in 2nd quadrant

Q 2 - The separation of the point A (- 5, 0) from the beginning is:

Answer : A

Explanation

OA = √ (0+5)²+ (0+0)²   = √ 25     = 5 unit.

Q 3 - In the event that the separation of the point p(x, y) from A (a, 0) is a+x, then y²=?

Answer : B

Explanation

(x-a) ²+(y-o) ²= a+x
⇒ (x-a) ²+y²= (a+x) ²⇒y²=(x+a) ²-(x-a) ²= 4ax ⇒ y²=4ax

Q 4 - The vertices of a triangle are A(4,4) ,B(3,- 2) ,C(- 3,16) . The range of the triangle is:

Answer : D

Explanation

Here x₁=4, x₂ = 3, Xᴈ = -3, y₁ =4, y₂= -2 and Yᴈ = 16
 ∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)]
 =1/2 [4(-2-16) +3(16-4)-3(4+2)]
 = 1/2 [(-72+36-18)] = 27 sq. units.

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

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 - The slop of a flat line is

Answer : A

Explanation

The slop of a horizontal line is m= tan ℴ =0

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 - 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=?

Answer : A

Explanation

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

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

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.

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