Coordinate Geometry

This chapter introduces coordinate geometry, the method of describing the position of a point in a plane using two numbers. It is based on the Cartesian system, named after the French mathematician Rene Descartes. You will learn that two perpendicular number lines, the horizontal x-axis and the vertical y-axis, meet at the origin O, whose coordinates are (0, 0), and divide the plane into four quadrants numbered I to IV in the anticlockwise direction. The x-coordinate or abscissa of a point is its perpendicular distance from the y-axis, and the y-coordinate or ordinate is its distance from the x-axis, measured with signs. You will learn the sign pattern of coordinates in each quadrant: positive and positive in quadrant I, negative and positive in II, negative and negative in III, and positive and negative in IV. Points on the x-axis have ordinate zero and points on the y-axis have abscissa zero. You will plot points, locate them from their coordinates, and see that (x, y) and (y, x) are different points unless x equals y.

Detailed Worksheet: Coordinate Geometry Section A - Definitions (10 marks) 1. What are the coordinate axes? What is the origin and what are its coordinates? (2 marks) 2. Define the abscissa and the ordinate of a point. (2 marks) 3. What are quadrants? How are they numbered? (2 marks) 4. Write the general form of the coordinates of a point on the x-axis and a point on the y-axis. (2 marks) 5. Write the sign of the abscissa and ordinate of a point in each of the four quadrants. (2 marks) Section B - Calculations and Applications (15 marks) 6. Name the quadrant or axis in which each point lies: (3, -5), (-2, 7), (-4, -6), (0, 8), (5, 0), (6, 2). (3 marks) 7. Write the coordinates of a point (i) 4 units to the left of the y-axis on the x-axis (ii) 3 units below the x-axis on the y-axis (iii) at a distance of 5 units from the x-axis and 2 units from the y-axis in quadrant II. (3 marks) 8. The points P(1, 1), Q(6, 1), R(6, 4) and S(1, 4) are the vertices of a quadrilateral. Plot them, name the figure and find its area. (3 marks) 9. Find the perpendicular distance of the point (-7, 3) from the x-axis and from the y-axis. Find the point that is its mirror image in the y-axis. (3 marks) 10. The vertices of a triangle are O(0, 0), A(6, 0) and B(0, 4). Name the type of triangle and find its area. (3 marks) Section C - Diagrams (10 marks) 11. Draw the Cartesian plane and plot the points (2, 3), (-3, 2), (-4, -1), (3, -2), (0, -4) and (5, 0). Label each point and its quadrant. (4 marks) 12. Plot the points (-2, 0), (2, 0), (2, 4) and (-2, 4). Join them in order and name the figure formed. Find its perimeter. (3 marks) 13. Plot the points (1, 2), (2, 4), (3, 6) and (4, 8). Join them. What do you observe about the points? (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Explain why the points (3, 5) and (5, 3) are different. Plot both and state in which case they would be the same point. (5 marks) 15. A rectangle has vertices A(-3, -2), B(4, -2), C(4, 3) and D. Find the coordinates of D, plot the rectangle and find its length, breadth and area. In which quadrants do the vertices lie? (5 marks) 16. A city map uses a grid where the town hall is at the origin. The school is at (3, 4), the hospital at (-5, 2), the park at (-2, -3) and the station at (6, -1), with 1 unit = 1 km. Plot the places, state the quadrant of each and find the shortest distance from the town hall to the school along the grid lines and along a straight line. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use graph paper with a suitable scale and label both axes.