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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 - On which pivot does the point (6, 0) lies?
Answer : A
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:
Answer : D
Explanation
AB2 = (7-3)2+ (4-1)2 = (42+32) = (16+9) =25 ⇒ AB= √25 = 5 unit.
Q 3 - P is a point on x-hub at a separation of 3 units from y-pivot on its right side. The co-ordinates of P are:
Answer : A
Explanation
Clearly, the co-ordinates of P are P (3, 0).
Q 4 - The focuses A (1,- 3) ,B(13,9) ,C(10,12) and D(- 2,0) taken all together are the vertices of :
Answer : A
Explanation
AB2= (13-1) 2+ (9+3) 2= (144+144) = 288. BC2= (10-13) 2+ (12-9) 2= (9+9) = 18 CD2= ((10+2) 2+ (12-0) 2= (144+144) = 288 AD2= (-2-1) 2+ (0+3) 2= (9+9) = 18 ∴ ab= cd and BC= AD Diag AC2= (10-1) 2+ (12+3) 2= (81+225) = 306 Diag BD2= (-2-13) 2+ (0-9) 2= (225+81) = 306 ∴Diag AC= Diag BD ∴ ABCD is a rectangle.
Q 5 - The vertices of a ∆ ABC are A (- 3, 0), B (5, - 2) and C (- 8, 5). The centroid of ∆ABC is:
Answer : B
Explanation
Centroid = {1/3 (x₁ +x₂+Xᴈ), 1/3
(y₁+y₂+yᴈ)} = {1/3(-3+5-8), 1/3 (0-2+5)}
= (-2, 1)
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:
Answer : A
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?
Answer : C
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 the line is
Answer : B
Explanation
When m=0, the line is vertical.
Q 9 - The mathematical statement of a line going through the focuses A(- 1,1) and B(2,- 4) is:
Answer : B
Explanation
The equation of the line is (y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁) i.e., (y-1)/(x+1) = -4-1/2+1 ⇒ (y-1)/(x+1) = -5/3 ⇒ 3y-3= -5x-5 ⇒ 5x+3y+2 = 0
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