Rectangular Cartesian Coordinates Test

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Rectangular Cartesian Coordinates Test - 10

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Question 1
4 / -1

If C is a point on the line segment joining A (-3, 4) and B(2, 1) such that AC = 2 BC, then the coordinate of C is

A
(1/3, 2)

B
(2, 1/3)

C
(2, 7)

D
(7, 2)

Solution
Question 2
4 / -1

The point on the line 3x + 4y = 5, which is equidistant from (1, 2) and (3, 4) is

A
(7, - 4)

B
(15, - 10)

C
(1/7, 8/7)

D
(0, 5/6)
Question 3
4 / -1

Consider, three points
P = [ - sin (β - α), - cos β],
Q = [cos (β - α), sin β]
and R = [cos (β - α + θ), sin (β - θ)]
where 0 < α, β , θ < π/4. Then,

A
P lies on the line segment RQ

B
Q lies on the line segment PR

C
R lies on the line segment QP

D
P, Q and R are non - collinear

Solution
Question 4
4 / -1

The x - co ordinate of the incentre of the triangle that has the coordinates of mid - points of its sides as (0, 1) (1, 1) and (1, 0 ) is

A
2 + √2

B
2 - √2

C
1 + √2

D
1 - √2
Question 5
4 / -1

The equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5 is

A
x² + y² + 17x + 19y - 50 = 0

B
x² + y² - 17x - 19y - 50 = 0

C
x² + y² + 17x - 19y - 50 = 0

D
x² + y² - 17x - 19y + 50 = 0
Question 6
4 / -1

The circumcentre of the triangle formed by the lines y = x, y = 2x and y = 3x + 4 is

A
(6, 8)

B
(6, - 8)

C
(3, 4)

D
(-3, - 4)
Question 7
4 / -1

Circumcentre of the triangle whose vertices are (0, 0), (3, 0) and (0, 4) is

A
(3/2, 2)

B
(2, 3/2)

C
(0, 0)

D
None of these
Question 8
4 / -1

The circumcentre of a triangle formed by the lines xy + 2x + 2y + 4 = 0 and x + y + 2 = 0, is

A
(-1, -1)

B
(0, -1)

C
(1, 1)

D
(-1, 0)
Question 9
4 / -1

If O( 0, 0 ), P( 3,4 ), Q( 6,0 ) be the vertices of the ∆OPQ.The point R inside ∆OPQ is such that the triangles OPR, PQR and OQR are of equal area. Then, the coordinates of R are

A
(4/3, 3)

B
(3, 2/3)

C
(3, 4/3)

D
(4/3, 2/3)
Question 10
4 / -1

If a vertex of a triangle is (1, 1) and the mid-points of two sides through the vertex are ( -1, 2) and (3, 2), then the centroid of the triangle is

A
(1, 7/3)

B
(1/3, 7/3)

C
(-(1/3), 7/3)

D
(-1, 7/3)

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Rectangular Cartesian Coordinates Test - 10

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Rectangular Cartesian Coordinates Test - 10

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Question 1

(1/3, 2)

(2, 1/3)

(2, 7)

(7, 2)

Solution

Question 2

(7, - 4)

(15, - 10)

(1/7, 8/7)

(0, 5/6)

Question 3

P lies on the line segment RQ

Q lies on the line segment PR

R lies on the line segment QP

P, Q and R are non - collinear

Solution

Question 4

2 + √2

2 - √2

1 + √2

1 - √2

Question 5

x2 + y2 + 17x + 19y - 50 = 0

x2 + y2 - 17x - 19y - 50 = 0

x2 + y2 + 17x - 19y - 50 = 0

x2 + y2 - 17x - 19y + 50 = 0

Question 6

(6, 8)

(6, - 8)

(3, 4)

(-3, - 4)

Question 7

(3/2, 2)

(2, 3/2)

(0, 0)

None of these

Question 8

(-1, -1)

(0, -1)

(1, 1)

(-1, 0)

Question 9

(4/3, 3)

(3, 2/3)

(3, 4/3)

(4/3, 2/3)

Question 10

(1, 7/3)

(1/3, 7/3)

(-(1/3), 7/3)

(-1, 7/3)

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x² + y² + 17x + 19y - 50 = 0

x² + y² - 17x - 19y - 50 = 0

x² + y² + 17x - 19y - 50 = 0

x² + y² - 17x - 19y + 50 = 0