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

A - 2ax

B - 4ax

C - 6ax

D - 8ax

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

A - A rectangle

B - a rhombus

C - a square

D - none of these

Answer : A

Explanation

vertices
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 (2, 3), B (5, ℏ) and C (6, 7) are collinear, then ℏ=?

A - 4

B - 6

C - - 3/2

D - 11/4

Answer : B

Explanation

Here x₁=2, x₂= 5, Xᴈ = 6, y₁ =3, y₂= ℏ and Yᴈ = 7
 ∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)]
 <= > 2(ℏ-7) +5(7-3) +6(3-ℏ) =0   4ℏ= 24  ℏ=6

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 - The slop of a vertical line is

A - 0

B - 1

C - not characterized

D - none of these

Answer : C

Explanation

The slop of a vertical line is not defined.

Q 8 - On the off chance that for a line m= tan ℴ<0, then

A - ℴ is intense

B - ℴ is inhumane

C - ℴ= 90⁰

D - none of these

Answer : D

Explanation

m tan ℴ <0 ⇒ ℴ is obtuse.

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:

A - x+y-8 = 0

B - x-y+8

C - x-y-8= 0

D - none of these

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 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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