Rectangular Cartesian Coordinates Test

Result

Rectangular Cartesian Coordinates Test - 8

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Weekly Quiz Competition

Question 1
4 / -1

If the area of the triangle with vertices (x, 0), (1, 1) and (0, 2) is 4 sq units, then the value of x is

A
- 2

B
- 4

C
- 6

D
8
Question 2
4 / -1

The area enclosed with the curve |x| + |y| = 1 is

A
1 sq units

B
2 √2 sq units

C
√2 sq unints

D
2 sq units
Question 3
4 / -1

The area ( in sq units) of the triangle formed by the lines x = 0, y = 0 and 3x + 4y = 12, is

A
3

B
4

C
6

D
12
Question 4
4 / -1

Three points are A ( 6, 3), B (- 3,5), C (4, -2) and P (x, y) is a point, then the ratio of area of ∆PBC and ∆ ABC is

A

B

C

D
None of the above
Question 5
4 / -1

A variable line passes through a fixed point ( a, ) and meets the coordinate axes in A and B. The locus of the point of intersection of lines through A ,B parallel to coordinate

A

B

C

D
Question 6
4 / -1

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 - cos θ) y = a sin θ and x sin θ - (1 + cos θ) y + a sin θ = 0 is

A
y = ± ax

B
x = ± ay

C
y² = 4x

D
x² + y² = a²
Question 7
4 / -1

A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is

A
x² + y² = 4

B
x² + y² = 16

C
x² + y² = 8

D
|x| + |y| = 8
Question 8
4 / -1

A variable line through the point (1/5, 1/5) cuts the coordinates axes in the points A and B. If the point P divides AB, internally in the ratio 3 : 1, then the locus of P is

A
3y + x = 20xy

B
y + 3x = 20xy

C
x + y = 20xy

D
3x + 3y = 20xy
Question 9
4 / -1

A variable x/a + y/b = 1 is such that a +b = 4. The locus of mind-point of the portion of the line intercepted between the axes is

A
x + y = 4

B
x + y = 8

C
x + y = 1

D
x + y = 2
Question 10
4 / -1

If a point P(4, 3) is shifted by a distance -√2 unit parallel to the line y = x, then coordinates of P in new position are

A
(5, 4)

B
(5 + √2, 4 + √2)

C
(5 - √2, 4 - √2)

D
None of these