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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 between the point A (b, 0) and B (0, a) is:
Answer : B
Explanation
AB = √ (b-0)2+ (0-a) 2 = √ b2+a2 = √a2+b2
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 (1,2) ,B(5,4) ,C(3,8) and D(- 1,6) taken all together are the vertices of
Answer : C
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 - The vertices of a triangle are A (3, 8), B (- 4, 2) and C (5, - 1). The region of ∆ ABC is:
Answer : B
Explanation
Here x₁=3, x₂= -4, Xᴈ = 5, y₁ =8, y₂= 2 and Yᴈ = -1 ∆ = 1/2 [x₁(y₂-Yᴈ) +x₂(Yᴈ-y₁) +Xᴈ (y₁-y₂)] =1/2 [3(2+1)-4(-1-8) +5(8-2)] = 1/2 (9+36+30) = 75/2 sq.unit.
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 - A line goes through the point (3, 5) and makes an edge of 135⁰with the x-pivot. The mathematical statement of the line is:
Answer : A
Explanation
The equation of the line is: Y-5/x-3 = tan 135⁰ = tan (180⁰-45⁰) = -tan 45⁰ =-1 ⇒ Y-5 =3-x = > x+y -8 = 0
Q 10 - The mathematical statement of a line passing through (3, 4) and parallel to x-pivot is:
Answer : C
Explanation
The equation of the line is y+4/x-3 = tan0= 0 ⇒ y+4 = 0