Aptitude - Co-ordinate Geometry Online 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.

Questions and Answers

Q 1 - In which quadrant does the point (- 5, 7) lies?

A - First

B - second

C - third

D - fourth

Answer : B

Explanation

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

Q 2 - On which pivot does the point (0, - 5) lies?

A - x-pivot

B - y-hub

C - xy-pivot

D - none of these

Answer : B

Explanation

The point (0,-5) lies on y axis. 

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 (- 3, 0), B (1, - 3) and C (4, 1) are the vertices of

A - An equilateral triangle

B - an isosceles right angle triangle

C - a scalene triangle

D - None of these

Answer : B

Explanation

AB2= (1+3) 2+ (-3-0) 2= 16+9= 25
BC2= (4-1) 2+ (1+3) 2=9+16= 25
AC2= (4+3) 2+ (1-0) 2= 49+1= 50
Clearly, AB= BC and AB2+BC2= AC2
∴ ∆ABC is ab isosceles right angle triangle.

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 - 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 - 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 - 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 - 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 lines 3x-4y+6 =0 and 4x+3y-10 =0 are mutually.

A - Parallel

B - perpendicular

C - opposite

D - none of these

Answer : D

Explanation

3x-4y+6 = 0 ⇒ 4y = 3x+6 ⇒ y =3x/4 +3/2
 4x+3y -10 =0 ⇒ 3y= -4x+10 ⇒ y = -4x/3 + 10/3
 ∴ m₁ = 3/4 and m₂ = -4/3. So, m₁m₂= -1

aptitude_coordinate_geometry.htm
Advertisements