**Importatant Terms, Definitions and Results**

- To locate the position of an object or a point in a plane, we require two perpendicular lines, one of them is horizontal and the other is vertical.
- The horizontal line is called the x-axis and the vertical line is called the y-axis.
- We call the plane, the cartesian plane, or the coordinate plane or the xy-plane. The axes are called the coordinate axes.
- The point of intersection of the axes (x-axis and y-axis) is called the origin.
- The coordinate axes divide the plane into four parts, called quadrants.
- The distance of a point from the y-axis is called its x-coordinate or abscissa. The distance of a point from the x-axis is called the y-coordinate or ordinate.
- If x ≠ y, then the position of (x, y) in the cartesian plane is different from the position of (y, x). It means the order of x and y is important in (x, y). Therefore, (x, y) is called an ordered pair.
- A point in a plane can be represented by an ordered pair (x, y), where x is the x-coordinate (abscissa) and y is the y-coordinate (ordinate) of the point.
- The coordinates of the origin are (0, 0).
- The coordinates of a point on the x-axis are of the form (x, 0) and that of a point on the y-axis are (0, y).
- A point in the first quadrant will be of the form (+, +). Similarly, a point in the second, third and fourth quadrants will be of the form (–, +), (–, –) and (+, –) respectively.

IX Maths: Coordinate Geometry: Assignment

**1 mark questions**1. The distance of the point (0, 8) from the origin is :

(a) 0 units (b) 8 units (c) cannot be determined (d) none of these

2. Which of the following points lies on the x-axis ?

(a) (0, 4) (b) (–5, –3) (c) (5, 0) (d) (0, 6)

3. The co-ordinates of a point are (x, y) and it lies in the 4th quadrant. Which of the following is true ?

(a) x > 0, y > 0 (b) x < 0, y < 0

(c) x > 0, y < 0 (d) x < 0, y > 0

4. Which of the following points lies below the x-axis ?

(a) (5, – 4) (b) (–5, 4) (c) (–3, 0) (d) (3, 0)

5. Which lies on the –ve x-axis ?

(a) (4, 0) (b) (– 4, 0) (c) (0, –4) (d) (0, 4)

1. Write the coordinates of a point which:-

(a) Lies on the x-axis and is at a distance of 4 units to the right of the origin.

(b) Lies on the y-axis and is at a distance of y units below the x-axis.

(c) Is at a distance of 3 units from the x-axis and 7 units from the y-axis. [there would be four such points]

2. Draw the graphs of 3x – 2y = 7 on the same pair of axes. Read the coordinates of their point of intersection.

3. Find the point where the line represented by the equation 5y – 3x – 10 = 0 cuts the y-axis.

4. Draw the graph of the line 3x + 4y = 18. With the help of graph find value of y when x = 2. (show this point on the graph)

5. On a graph draw a quadrilateral whose vertices are (1,1), (2,4), (8,4) and (10,1). Justify the quadrilateral.

6. Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

7. in which quadrant will the point lie, if:-

(a) ordinate is 3 and abscissa is – 7

(b) abscissa is – 10 and ordinate is – 4

(c) Ordinate is 4 and abscissa is – 6.

8. Fill in the blanks:-

(a) The coordinates of the origin 0 are ………………………

(b) The y coordinate of every point on the x-axis is ……………

(c) Distance along the x-axis is called ………………………

(d) Distance along the y-axis is called ………………………

(e) The point (x,y) = (y,x) only if ………………………

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

co-ordinates of the fourth vertex.

10. 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.

(a) 0 units (b) 8 units (c) cannot be determined (d) none of these

2. Which of the following points lies on the x-axis ?

(a) (0, 4) (b) (–5, –3) (c) (5, 0) (d) (0, 6)

3. The co-ordinates of a point are (x, y) and it lies in the 4th quadrant. Which of the following is true ?

(a) x > 0, y > 0 (b) x < 0, y < 0

(c) x > 0, y < 0 (d) x < 0, y > 0

4. Which of the following points lies below the x-axis ?

(a) (5, – 4) (b) (–5, 4) (c) (–3, 0) (d) (3, 0)

5. Which lies on the –ve x-axis ?

(a) (4, 0) (b) (– 4, 0) (c) (0, –4) (d) (0, 4)

**2 and 3 marks questions**1. Write the coordinates of a point which:-

(a) Lies on the x-axis and is at a distance of 4 units to the right of the origin.

(b) Lies on the y-axis and is at a distance of y units below the x-axis.

(c) Is at a distance of 3 units from the x-axis and 7 units from the y-axis. [there would be four such points]

2. Draw the graphs of 3x – 2y = 7 on the same pair of axes. Read the coordinates of their point of intersection.

3. Find the point where the line represented by the equation 5y – 3x – 10 = 0 cuts the y-axis.

4. Draw the graph of the line 3x + 4y = 18. With the help of graph find value of y when x = 2. (show this point on the graph)

5. On a graph draw a quadrilateral whose vertices are (1,1), (2,4), (8,4) and (10,1). Justify the quadrilateral.

6. Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

7. in which quadrant will the point lie, if:-

(a) ordinate is 3 and abscissa is – 7

(b) abscissa is – 10 and ordinate is – 4

(c) Ordinate is 4 and abscissa is – 6.

8. Fill in the blanks:-

(a) The coordinates of the origin 0 are ………………………

(b) The y coordinate of every point on the x-axis is ……………

(c) Distance along the x-axis is called ………………………

(d) Distance along the y-axis is called ………………………

(e) The point (x,y) = (y,x) only if ………………………

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

co-ordinates of the fourth vertex.

10. 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.

9th Co -Ordinate geometry Test Paper

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