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 (- 5, 0) from the beginning is:
Answer : A
Explanation
OA = √ (0+5)2+ (0+0)2 = √ 25 = 5 unit.
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,- 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 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 - 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)
Answer : A
Explanation
The slop of a horizontal line is m= tan ℴ =0
Q 8 - A line goes through the focuses A (- 2, 3) and B (- 6, 5). The slop of line AB is
Answer : A
Explanation
Slop = (y₁ ?y₂)/( x₁-x₂) = (5-3)/(-6+2) = 2/-4 =-1/2
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 x+2y-9 =0 and 3x+6y+8 =0 are commonly.
Answer : A
Explanation
x+2y-9 =0 ⇒ 2y = -x+9 ⇒ y= -x/2+9/2 3x+6y+8 =0 ⇒ 6y= -3x-8 ⇒ y=-x/2 -4/3 ∴ m₁: m₂ = -1/2 Hence, the given lines are parallel.
