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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.

Q 1 - In which quadrant does the point (4, - 6) lies?

Answer : D

Explanation

The point (4,-6) lies in 4th quadrant

Q 2 - The separation of the point p (8, - 6) from the beginning is:

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:

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=?

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 A (6, 4) and B (- 2, 2) and its centroid is G (3, 4). The directions of C are:

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 flat line is

Answer : A

Explanation

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

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

Answer : C

Explanation

m tan ℴ>0 ⇒ℴ is acute.

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.

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

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