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 (- 3, - 5) lies?

A - First

B - second

C - third

D - fourth

Answer : C

Explanation

The point (-3,-5) lies in 3rd 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 vertices of a triangle are A(4,4) ,B(3,- 2) ,C(- 3,16) . The range of the triangle is:

A - 36 sq. unit

B - 37 sq.unit

C - 38 sq. unit

D - none of these

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 - The vertices of a triangle are A (3, 8), B (- 4, 2) and C (5, - 1). The region of ∆ ABC is:

A - 57/2 sq. unit

B - 75/2 sq. unit

C - 57 sq. unit

D - 75 q. units

Answer : B

Explanation

Here x₁=3, x₂= -4, Xᴈ = 5, y₁ =8, y₂= 2 and Yᴈ = -1
 ∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)]
 =1/2 [3(2+1)-4(-1-8) +5(8-2)] = 1/2 (9+36+30) = 75/2 sq.unit.

Q 6 - Two vertices of a ∆abc are A (6, 4) and B (- 2, 2) and its centroid is G (3, 4). The directions of C are:

A - (4, 5)

B - (5, 3)

C - (5, 6)

D - (- 3, 3)

Answer : C

Explanation

  Let the co- ordinates of C be (a, b). Then,
 1/3 (6-2+a) =3 and 1/3 (4+2+b) =4
 4+a=9 and 6+b=12  ⇒ a=5, b= 6

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 - A line goes through the focuses A (- 2, 3) and B (- 6, 5). The slop of line AB is

A - - 1/2

B - 1/2

C - 3/4

D - -1

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:

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 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

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