# 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 - On which pivot does the point (6, 0) lies?

A - x-pivot

B - y-hub

C - xy-pivot

D - none of these

### Explanation

`The point lies on (6, 0) lies on x-axis.`

Q 2 - The separation of the point A (7, 4) and B (0, a) is:

A - 6 units

B - 3 units

C - 4 units

D - 5 unit

### Explanation

`AB2 = (7-3)2+ (4-1)2 = (42+32) = (16+9) =25 ⇒ AB= √25 = 5 unit.`

Q 3 - The separation of the point A (2, - 3) and B (2, 2) is:

A - 2 units

B - 3 units

C - 4 units

D - 5 unit

### Explanation

`AB2= (2-2) 2+ (-3-2) 2= 0+25=25 ⇒ AB =√ 25 =5 unit`

Q 4 - The focuses A (1,2) ,B(5,4) ,C(3,8) and D(- 1,6) taken all together are the vertices of

A - A rectangle

B - a rhombus

C - a square

D - none of these

### Explanation

``` AB2= (5-1) 2+ (4-2) 2= (16+4) = 20
BC2= (3-5) 2+ (8-4) 2= (4+16) = 20
CD2= (-1-3) 2+ (6-8) 2= (16+4) = 20
DA2= (1+1) 2+ (2-6) 2= (4+16)=20
∴ AB= BC= CD= DA= √20
Diagonal AC2= (3-1) 2+ (8-2) 2= (4+36) = 40
Diagonal BD2= (-1-5) 2+ (6-4) 2= (36+4) = 40
∴ Diag AC= Diag BD =√40
∴ ABCD is a square.```

Q 5 - In the event that the focuses A(1,- 1) , B(5,2) and C(ℏ,5) are collinear , then ℏ=?

A - 6

B - -3

C - 0

D - 4

### Explanation

```Here x₁=1, x₂= 5, Xᴈ = ℏ, y₁ =-1, y₂= 2 and Yᴈ = 5
∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)]
 1. (2-5) +5(5+1) +ℏ (-1-2) = 0
 -3+30-3ℏ=0   3ℏ =27  ℏ =0```

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)

### 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 - 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 - The slop of a line going through the focuses A (4, 3) and B (6, 3) is:

A - 2

B - ∞

C - 0

D - none of these

### Explanation

`Slop = (y₁ ?y₂)/( x₁-x₂) = (-3+3)/(6-4) =0/2 =0`

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=?

A - 5

B - -5

C - 8

D - 10

### 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

A - ℏ= 2

B - ℏ= 1

C - ℏ= - 1

D - ℏ = - 2

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