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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 (- 3, - 5) lies?

Answer : C

Explanation

The point (-3,-5) lies in 3rd quadrant

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

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:

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 - 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 - y-pivot partitions the join of P (- 4, 2) and Q (8, 3) in the proportion

Answer : D

Explanation

Let the required ratio be ℏ:1. Then, its co-ordinates are [(8ℏ -4 / ℏ +1, 3ℏ +2/ℏ +1)]
 But lies on y-axis. So, its abscissa is 0.
 ∴ 8ℏ  -4 / ℏ +1=0  ⇒ 8ℏ  -4  =0 ⇒ ℏ =1/2
Required ratio is 1/2:1, i.e. 1:2

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

Answer : B

Explanation

When m=0, the line is vertical.

Q 9 - On the off chance that the slant of a line joining the focuses A(x,- 3) and B(2,5) is 135⁰ then x=?

Answer : D

Explanation

Slop of AB = (5+3)/(2-x) =8/2-x
 ∴ 8/2-x = tan135⁰ = tan (180⁰- 45⁰) = -tan 45⁰ =-1 
8/2-x = -1 ⇒8 = x-2 ⇒ x= 10

Q 10 - The estimation of ℏ for which the line x+2y-9= 0 and ℏx+4y+5 =0 are parallel, is

Answer : A

Explanation

Since the given lines are parallel, we have 1/ℏ =2/4 ⇒ ℏ = 2

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