Finding the Coordinates of a Point

Q.

Question 2 (i)
(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

how many cross-streets can be referred to as (4, 3)?

Q. Let R be a relation defined on set A = {1, 2, 3, 4} such that R={(1, 2) (1, 3) (2, 4) (3, 2)} if domain of R is the set B and range is the set C then find ( B intersection C )

Q.

An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q. What are the coordinates of points P and Q?

1. P(3, 0); Q(3, -4)

2. P(0, 3); Q(3, 4)

3. P(0, 3); Q(4, -3)

4. P(-3, 0); Q(-3, 4)

Q.

Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinate of the point R such that PQRS is a square.

Q. The distance of a point (0, -5) from the origin is ____.

1. 6 units
2. -5 units
3. 5 units
4. 0 units

Q.

If A = [(x, y): $x^2+y^2=25$] And B = [(x, y): $x^2+9y^2=144],thenA\cap B$ contains

1. Three points

2. Two points

3. One point

4. Four points

Q.

A point is at a distance of 3 units from the x-axis and 5 units from the y-axis. Which of the following are the coordinates of the point?

1. (5, 3)

2. (–5, 3)

3. (–3, –5)

4. (3, 5)

Q. Find the area of the figure formed by joining the points A, B, C, and D.

1. 10 square units
2. 25 square units
3. 15 square units
4. 30 square units

Q. The perpendicular distance of point P(7, 3) from the y-axis is ___.

1. 0 units
2. 4 units
3. 7 units
4. 3 units

Q.

Question 1
How will you describe the position of a table lamp on your study table to another person?

Q. If I move 5 units towards the east direction and then move 7 units towards the north direction starting from the origin. What will be my coordinates?
(positive x - axis = Direction of east)

1. (5, -7)
2. (-5, 7)
3. (5, 7)
4. (-5, -7)

Q. The perpendicular distance of the point A(7, 5) from y-axis is
(a) 7 units
(b) 5 units
(c) 12 units
(d) 2 units

Q.

Question 2 (ii)
(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

how many cross-streets can be referred to as (3, 4)?

Q.

An ant struggling for food finds it at the north-east corner of the Cartesian plane. It moves 3 units east from the origin and then 3 units north. Find the location of the food.

1. (-3, 3)

2. (3, 3)

3. (-3, -3)

4. (3, -3)

Q. What is the difference between the ordinate of point A and B?

1. 0
2. 3
3. 6
4. 9

Q. The perpendicular distance of the point P(4, 3) from the y-axis is
(a) 3 units
(b) 4 units
(c) 5 units
(d) 7 units

Q. An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q.
(i) What are the coordinates of points P and Q?
(ii) Also, find the distance between the point P and Q.

[4 Marks]

Q. The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

Q. A worm starts moving 5 units from the origin towards the positive x - axis and then it moves 6 units towards the negative y - axis and then it moves 8 units towards the negative x - axis to complete its journey. What will be the coordinates of the worm after it completes its journey?

1. (3, -6)
2. (- 3, - 6)
3. (-5, -8)
4. (5, -8)

Q. ABCD is a square in which the coordinates of A are (-2, 4), C are (4, 10), D are (-2, 10)
Find the coordinates of B.

Q.

Question 2 (i)
Write the coordinates of B.

Q.

Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axis.

x	− 2	− 1	0	1	3
y	8	7	−1.25	3	− 1

Q.

Question 2 (ii)
Write the coordinates of C.

Q. An ant starts from the origin on a Cartesian plane and moves 5 units east and then 3 units north. Find the coordinates of the location of ant.

Q. The three vertices of a square ABCD are A(3, 2) B(−2, 2) and D(3, −3). Plot these points on a graph paper and hence, find the coordinates of C. Also, find the area of square ABCD.

Q. A point is at a distance of 3 Units from the x-axis and 5 units from y-axis. Which of the following are the coordinates of the point?

Q. What is the difference between the abscissa of point A and that of B?

1. 0
2. 6
3. 2
4. 3

Q. Points A(5, 3), B(-2, 3) and D(5, -4) are three vertices of a square ABCD. Find the coordinates of the vertex C.

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

Q.

Puppy says that the point P (5, 6) is same as the point Q (6, 5). Is he correct?

1. False

2. True

Q. Find the co-ordinates of the centre of a circle passing through the points A(3, 5) B($-$1, 2) and C(3, $-$3). Also find the radius of circle.