Co-ordinate Geometry

Three vertices of a rectangle are (3, 2), (– 4, 2) and (– 4, 5). Plot these points and find the coordinates of the fourth vertex.

Plot the point P (– 6, 2) and from it draw PM and PN as perpendiculars to x-axis and y-axis, respectively. Write the coordinates of the points M and N

Write whether the following statements are True or False? Justify your answer.

(i) Point (0, –2) lies on y-axis. (ii) The perpendicular distance of the point (4, 3) from the x-axis is 4.

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), S (2, 2)

Plot the following points and check whether they are collinear or not:

(i) (1, 3), (– 1, – 1), (– 2, – 3) (ii) (1, 1), (2, – 3), (– 1, – 2) (iii) (0, 0), (2, 2), (5, 5)

Without plotting the points indicate the quadrant in which they will lie, if

(i) ordinate is 5 and abscissa is – 3 (ii) abscissa is – 5 and ordinate is – 3

(iii) abscissa is – 5 and ordinate is 3 (iv) ordinate is 5 and abscissa is 3

In which quadrant or on which axis each of the following points lie?

(– 3, 5), (4, – 1), (2, 0), (2, 2), (– 3, – 6)

Which of the following points lie on y-axis? A(1, 1), B(1, 0), C(0, 1), D(0, 0), E(0, – 1), F(– 1, 0), G(0, 5), H(– 7, 0), I(3, 3).

A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates? What will be the coordinates if it lies on y-axis at a distance of –7 units from x-axis?

Find the coordinates of the point (i) which lies on x and y axes both. (ii) whose ordinate is – 4 and which lies on y-axis. (iii) whose abscissa is 5 and which lies on x-axis.

Taking 0.5 cm as 1 unit, plot the following points on the graph paper: A(1, 3), B(– 3, – 1), C(1, – 4), D(– 2, 3), E(0, – 8), F(1, 0)

Point (–3, 5) lies in the (A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant

Signs of the abscissa and ordinate of a point in the second quadrant are respectively (A) +, + (B) –, – (C) –, + (D) +, –

Point (0, –7) lies (A) on the x –axis (B) in the second quadrant (C) on the y-axis (D) in the fourth quadrant

Point (– 10, 0) lies (A) on the negative direction of the x-axis (B) on the negative direction of the y-axis (C) in the third quadrant (D) in the fourth quadrant

Abscissa of all the points on the x-axis is (A) 0 (B) 1 (C) 2 (D) any number

Ordinate of all points on the x-axis is (A) 0 (B) 1 (C) – 1 (D) any number

The point at which the two coordinate axes meet is called the (A) abscissa (B) ordinate (C) origin (D) quadrant

A point both of whose coordinates are negative will lie in (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) (A) lie in II quadrant (B) lie in III quadrant (C) lie in IV quadrant (D) do not lie in the same quadrant

If y coordinate of a point is zero, then this point always lies (A) in I quadrant (B) in II quadrant (C) on x - axis (D) on y – axis

The points (–5, 2) and (2, – 5) lie in the (A) same quadrant (B) II and III quadrants, respectively (C) II and IV quadrants, respectively (D) IV and II quadrants, respectively

If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has (A) x – coordinate = – 5 (B) y - coordinate = 5 only (C) y – coordinate = – 5 only (D) y – coordinate = 5 or –5

On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained? (A) Square (B) Rectangle (C) Trapezium (D) Rhombus

If P (– 1, 1), Q (3, – 4), R(1, –1), S(–2, –3) and T (– 4, 4) are plotted on the graph-paper, then the point(s) in the fourth quadrant are (A) P and T (B) Q and R (C) Only S (D) P and R

If the coordinates of the two points are P (–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is (A) – 5 (B) 1 (C) – 1 (D) – 2

If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are (A) P and R (B) R and S (C) Only Q (D) Q and O

Abscissa of a point is positive in (A) I and II quadrants (B) I and IV quadrants (C) I quadrant only (D) II quadrant only

The point whose ordinate is 4 and which lies on y-axis is?

(A) (4, 0) (B) (0, 4) (C) (1, 4) (D) (4, 2)

Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x–axis? (A) P and R only (B) Q and S only (C) P, R and T (D) Q, S and T

The perpendicular distance of the point P (3, 4) from the y – axis is (A) 3 (B) 4 (C) 5 (D) 7

(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 about 5 streets in each direction. Using 1 cm = 100 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:

(i) How many cross - streets can be referred to as (4, 3).

(ii) How many cross - streets can be referred to as (3, 4).

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

In which quadrant or on which axis do each of the points and lie? Verify your answer by locating them on the Cartesian plane.

See the given figure, and write the following:

(i) The coordinates of B.

(ii) The coordinates of C.

(iii) The point identified by the coordinates.

(iv) The point identified by the coordinates

(v) The abscissa of the point D.

(vi) The ordinate of the point H.

(vii) The coordinates of the point L.

(viii) The coordinates of the point M

Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(ii) What is the name of each part of the plane formed by these two lines?

(iii) Write the name of the point where these two lines intersect.

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