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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.
Answer : B
Explanation
The point (-5, 7) lies in 2nd quadrant
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 - In the event that the separation of the point p(x, y) from A (a, 0) is a+x, then y2=?
Answer : B
Explanation
(x-a) 2+(y-o) 2= a+x ⇒ (x-a) 2+y2= (a+x) 2⇒y2=(x+a) 2-(x-a) 2= 4ax ⇒ y2=4ax
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 - In the event that the focuses A(1,- 1) , B(5,2) and C(ℏ,5) are collinear , then ℏ=?
Answer : C
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 - A point C partitions the join Of A (1, 3) and B (2, 7) in the proportion 3:4. The co-ordinates of C are:
Answer : C
Explanation
Co-ordinates of C are [(5*2+4*1/3+4), (3*7+4*3/ 3+4) i.e. (10/7, 33/7)
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
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:
Answer : C
Explanation
Slop = (y₁ ?y₂)/( x₁-x₂) = (2+1)/ (3-3) = 3/0, which is not defined
Q 10 - The point made by the line x+√3y-6 =0 with positive course of x-pivot is
Answer : B
Explanation
x+√3y-6= 0 ⇒ √3y= -x+6 ⇒ y = -1x/ √3+ 6/√3 ∴ m = tan ℴ =-1/√3 = -tan 30⁰ = tan (180⁰-30⁰) = tan150⁰ ∴ ℴ = 150⁰