Rectangular Cartesian Coordinates Test

Result

Rectangular Cartesian Coordinates Test - 27

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Weekly Quiz Competition

Question 1
4 / -1

If O be the origin and if the co-ordinates of any two points Q₁ and Q₂ be (x₁, y₁) and (x₂, y₂) respectively. Then OQ₁ ∙ OQ₂ cos Q₁OQ₂ =

A
x₁ x₂ – y₁ y₂

B
x₁ y₁ – x₂ y₂

C
x₁ x₂ + y₁ y₂

D
x₁ y₂ + x₂ y₂

Solution
Question 2
4 / -1

Given the points A(0,4) and B(0,4). Then the equation of the locus of the point P(x,y) such that |AP - BP) = 6 is

A

B

C

D

Solution
Question 3
4 / -1

If ABCD is a quadrilateral, if the mid point of consecutive sides AB, BC, CD and DA are combined by straight lines, then the quadrilateral PQRS is always

A
Square

B
parallelogram

C
Rectangle

D
Rhombus
Question 4
4 / -1

A(a,0) and B(-a,0) are two fixed points of triangle ABC. The vertex C moves in such a way that cot A + cot B = λ , where λ is a constant.Then the locus of the point C is

A
yλ = 2a

B
ya = 2λ

C
y = λa

D
None of these

Solution
Question 5
4 / -1

A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is the same, then in the ∆ABC, the foot of the pole is at the

A
Centroid

B
Circumcentre

C
Incentre

D
Orthocentre

Solution
Question 6
4 / -1

The point A divides the join of the points (-5,1) and (3,5) in the ratio k : 1and the co-ordinates of the points B and C are (1,5) and (7,-2) respectively. If the area of the triangle ABC be 2 units , then k =

A
6,7

B

C

D
7,9

Solution
Question 7
4 / -1

The area of a triangle is 5. If two of its vertices are (2,1), (3,-2) and the third vertex lies on the line y = x + 3, then the third vertex is

A

B

C

D

Solution
Question 8
4 / -1

P(3,1) , Q(6,5) and R (x,y) are three points such that the angle PRQ is a right angle and the area of the ∆RPQ = 5, then the number of such points R is

A
0

B
1

C
2

D
4

Solution
Question 9
4 / -1

A

B

C

D

Solution
Question 10
4 / -1

The points P is equidistant from A(1,3) , B(-3,5) and C(5,-1). Then PA =

A
5

B

C
25

D

Solution