Cartesian system

Q. Point (-3, 4) lies in 3rd quadrant

1. False
2. True

Q. In which quadrant does the point (5, -6) lie?

1. $1^{st}$ Quadrant
2. $4^{th}$ quadrant
3. $3^{rd}$ quadrant
4. It doesn’t lie in any quadrant

Q. Question 2
Plot the following points and write the name of the figure obtained by joining, them in order.
P(-3, 2), Q(-7, -3), R(6, -3) and S(2, 2).

Q. If the coordinates of a point M are (-2, 9) which can also be expressed as$(1+x,y^2)$ and y > 0, then find in which quadrant do the following points lie : P(y, x), Q(2, x), $R(x^2,y-1)$, S(2x, -3y).

Q. Find the image of point (2, 3) under the line x-axis.

Q.

The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-2, 0) then the distance of point B from the origin is ___ units.

Q. What are the coordinates of the points that lie in the second quadrant?

1. (-3, -2), (-1, -3), and (-3, -5)
2. (2, 3), (3, 1) and (5, 3)
3. (2, -2), (3, -3) and (2, -5)
4. (-3, 4), (-2, 3) and (-4, 1)

Q. Point (-3, 4) lies in 3rd quadrant

1. False
2. True

Q.

What is the difference between the ordinates of the points (−2, 3) and (5, 8)?

1. 5

2. 7

3. 10

4. 3

Q. If point P (x, y) falls in the ${II}^{nd}$ quadrant then what will be the sign of x and y?

1. (-, +)
2. (+, +)
3. (-, -)
4. (+, -)

Q.

Answer the following questions: [3 MARKS]

(a) In which quadrant will the point lie, if the abscissa is –10 and the ordinate is – 4.
(b) Draw a rectangle PQRS in which vertices P, Q, R and S are (1, 4), (-5, 4), (-5, -3) and (1, -3) respectively.

Q.

The distance of any point from the $y-\mathrm{axis}$ is the __________ coordinate.

Q.

Which of the points lie in the IV quadrant?

1. True

2. False

3. (2, -4)
4. (0.2, -100 )

Q.

In which quadrant or on which axis do each of the points (3, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane
[4 MARKS]

Q. Which of the following graph shows the correct plotting of point P(-2, 3)?

1. 
2. 
3. 
4. 

Q. A point whose abscissa and ordinate are 2 and −5 respectively, lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Q. In which quadrant or on which axis do each of the points (−2, 4), (3, −1), (−1, 0), (−3, −5) and (0, −1) lie?

Q.

All points with $y-$coordinate as zero lie on the ____________

Q. For $x=2,y=-1,u=3,v=2$ the point $(x\times y,u\times v)$ will lie in which quadrant?

1. I quadrant
2. II quadrant
3. III quadrant
4. IV quadrant

Q.

The dependent variables are typically represented in which of the following positions in a Cartesian co-ordinate system?

1. Quadrant

2. x-axis

3. y-axis

4. Origin

Q. A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the point B if AB and BC are parallel to the coordinate axes.

1. (3, 2)
2. (5, 4)
3. (1, 1)
4. (2, 1)

Q. The points on the x-axis that are to the left of the origin are.

1. positive
2. negative
3. zero

Q. For $p=4,q=5,u=4,v=-3$ the point $(p+q,u\times v)$ will lie in which quadrant?

1. I quadrant
2. II quadrant
3. III quadrant
4. IV quadrant

Q.

Use the following information to answer the next question

What are the respective coordinates of points A and B in the given graph?

1. (3, −1) and (2, −3)

2. (3, 1) and (−3, −2)

3. (1, 3) and (−2, −3)

4. (−1, 3) and (−2, 3)

Q.

The perpendicular bisector of a line segment AB passes through the origin. If the coordinates of A are (-3, 0) then the distance of point B from the origin is ___ units.

1. 0

2. 1

3. -1

4. Any number

Q. Match the following columns:

Column I	Column II
(a) The point A(−3, 0) lies on	(p) y-axis
(b) The point B(−5, −1) lies in quadrant	(q) IV
(c) The point C(2, −3) lies in quadrant	(r) III
(d) The point D(0, −6) lies on	(s) x-axis

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Q. Which of the following are the coordinates of the point whose ordinate is 6 and abscissa is -3?

1. (6, -3)
2. (-3, 6)
3. (3, 6)
4. (6, 3)

Q. Point (0, 7) lies on the x-axis.

1. False
2. True

Q. Points A(5, 3) B(-2, 3) and D(5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence, find the coordinates of the vertex C. (2 marks)

Q.

the transverse axis of a hyperbola lies along the x-axis and its center is at the origin. the length of the conjugate axis is 8 and the point (3, 3) lies on the hyperbola.

find its eccentricity and the length of latus rectum.