# 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 (- 5, 7) lies?

A - First

B - second

C - third

D - fourth

### 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

### 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

### 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

### 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

### 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)

### 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

### 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

### 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

### 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

```3x-4y+6 = 0 ⇒ 4y = 3x+6 ⇒ y =3x/4 +3/2