1 / 34

Coordinate Geometry

Coordinate Geometry. The Cartesian Plane and Gradient. Basic Terminology. The figure on the right shows 2 perpendicular lines intersecting at the point O . This is called the Cartesian Plane . O is also called the origin .

vega
Download Presentation

Coordinate Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Coordinate Geometry The Cartesian Plane and Gradient

  2. Basic Terminology • The figure on the right shows 2 perpendicular lines intersecting at the point O. This is called the Cartesian Plane. • O is also called the origin. • The horizontal line is called the x-axis and the vertical line is called the y-axis

  3. The position of any point in the Cartesian Plane can be determined by its distance from each axes. Example: Point A is 3 units to the right of the y-axis and 1 unit above the x-axis, its position is described by the coordinate(3, 1). Similarly, the coordinates of Points B, C and D are determined as shown. Coordinates of a Point

  4. Question • What coordinate represents the origin O ? • Ans: (0, 0)

  5. Summary • Any point, P, in the plane can be located by it’s coordinate (x, y). • We call x the x - coordinate of P and y the y - coordinate of P. • Hence, we say that P has coordinates (x, y).

  6. Solution to Exercise 1

  7. The steepness of a line is called its GRADIENT (or slope). The gradient of a line is defined as the ratio of its vertical distance to its horizontal distance. l Gradient (or slope)

  8. Examples of Gradient What is the gradient of the driveway? Ans: Note: Gradient has no units!

  9. Examples of Gradient An assembly line is pictured below. What is the gradient of the sloping section? Ans:

  10. Examples of Gradient The bottom of the playground slide is 2.5 m from the foot of the ladder. The gradient of the line which represents the slide is 0.68. How tall is the slide? Ans:

  11. Question For safety considerations, wheelchair ramps are constructed under regulated specifications. One regulation requires that the maximum gradient of a ramp exceeding 1200 mm in length is to be (a) Does a ramp 25 cm high with a horizontal length of 210 cm meet the requirements? (b) Does a ramp with gradient meet the specifications? (c) A 16 cm high ramp needs to be built. Find the minimum horizontal length of the ramp required to meet the specifications. Ans: No Ans: Yes Ans: 224 cm

  12. Horizontal and Vertical Lines • The gradient of a horizontal line is ZERO (Horizontal line is flat – No Slope) • The gradient of a vertical line is INIFINITY (Vertical line – gradient is maximum)

  13. Finding the gradient of a straight line in a Cartesian Plane (a) Positive Gradients • Lines that climb from left to the right are said to havepositive gradient/slope: (b) Negative Gradients • Lines that descend from left to the right are said to have negative gradient/slope:

  14. Examples Write down the coordinates of the points given (16, 0) (0, 10) (0, -8) (-15, 0)

  15. Examples (-4, 0) (0, 6) (3, 0) (0, -12)

  16. Summary Infinite

  17. Gradient Formula So far, we have determined the gradient using the idea of Using the above, we must always remember to add a negative sign to slopes with negative gradient. Now, let’s look at the formula to determine gradient. The formula will take into consideration the sign of the slope

  18. Gradient Formula y B(x2,y2) y2 Vertical = y2 – y1 A(x1,y1) y1 Horizontal = x2 – x1 x x1 x2

  19. How to apply gradient formula • Write down the coordinates of 2 points on the line: (x1, y1) and (x2, y2) • If the coordinate is negative, include its sign • Apply the formula

  20. Examples: (1, 4) L1: 2 points on the line are (1, 4) and (0, 1) (0, 1) Tip: Choose points that are easy to read! 1 square represents 1 unit on both axes

  21. (3, 3) (1, 1) Examples: L2: 2 points on the line are (1, 1) and (3, 3) Tip: Choose points that are easy to read! 1 square represents 1 unit on both axes

  22. (3, 1) (1, 0) Examples: L3: 2 points on the line are (3, 1) and (1, 0) 1 square represents 1 unit on both axes

  23. (3, -1) (-3, -3) Examples: L4: 2 points on the line are (3, -1) and (-3, -3) 1 square represents 1 unit on both axes

  24. (0, 1) (1, -2) Examples: L5: 2 points on the line are (0, 1) and (1, -2) 1 square represents 1 unit on both axes

  25. (-4, 4) (0, 0) Examples: L6: 2 points on the line are (0, 0) and (-4, 4) 1 square represents 1 unit on both axes

  26. (-2, 2) (4, -2) Examples: L7: 2 points on the line are (4, -2) and (-2, 2) 1 square represents 1 unit on both axes

  27. (-3, -1) (0, -2) Examples: L8: 2 points on the line are (0, -2) and (-3, -1) 1 square represents 1 unit on both axes

  28. Question Is there a difference between Ans: No. • Is there a difference between Ans: Yes!

  29. Solution to Exercise 2 In order from smallest to largest gradient: e, b, a, d, c

  30. 3 Horizontal Line: Zero Vertical Line: Inifinity

More Related