Plotting of points in the cartesian plane: |
• In the Cartesian plane, the horizontal line is called the x-axis and the vertical line is called the y-axis, |
• The coordinate axes divide the plane into four parts called quadrants, |
• The point of intersection of the axes is called the origin, |
• Abscissa or the x-coordinate of a point is its distance from the y-axis and the ordinate or the y-coordinate is its distance from the x-axis, |
• (x, y) are called the coordinates of the point whose abscissa is x and the ordinate is y, |
• Coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis is of the form (0, y), |
• The coordinates of the origin are (0, 0), |
• Sign of the coordinates of a point in the first quadrant are (+, +), in the second |
quadrant (–, +), in the third quadrant (–, –) and in the fourth quadrant (+, –). |
Write the correct answer in each of the following : |
1. Point (–3, 5) lies in the |
(A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant |
2. Signs of the abscissa and ordinate of a point in the second quadrant are respectively |
(A) +, + (B) –, – (C) –, + (D) +, – |
3. Point (0, –7) lies |
(A) on the x –axis (B) in the second quadrant (C) on the y-axis (D) in the fourth quadrant |
4. 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 |
5. Abscissa of all the points on the x-axis is |
(A) 0 (B) 1(C) 2 (D) any number |
6. Ordinate of all points on the x-axis is |
(A) 0 (B) 1 (C) – 1 (D) any number |
7. The point at which the two coordinate axes meet is called the |
(A) abscissa (B) ordinate (C) origin (D) quadrant |
8. A point both of whose coordinates are negative will lie in |
(A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant |
9. 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 |
10. 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 |
11. 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 |
12. 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 |
13. 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 |
14. 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 |
15. 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 |
16. 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 |
17. 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 |
Answers 1. (B) 2. (C) 3. (C) 4. (A) 5. (D) 6. (A) 7. (C) 8. (C) 9. (D) 10. (C)11. (C) 12. (D) 13. (B) 14. (B) 15. (B) 16. (D) 17. (B) |
2 MARKS QUESTIONS |
1. 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. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant. |
3. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square. |
4. Plot the points A (1, – 1) and B (4, 5) |
(i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B. |
(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB. |
ANSWERS |
1. C(–2, – 4) 2. (0, 0), (–5, 0), (0, –3) 3. (4, 3) 4. (i) (2, 1), (ii) (5, 7) |
