1. Chapter 10 Coordinate Treatment of Simple Locus Problems

2. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Path of a Moving Point (I) Given that P is a point on a wheel, what is the path of P when the wheel rolls on the ground?

3. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Path of a Moving Point (II) Given that P is a vertex of a rectangle, What is the path of P if the rectangle rolls on the horizontal level?

4. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Path of a Moving Point (III) Given that P is a vertex of a triangle, What is the path of P if the triangle rolls on the horizontal level?

5. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Locus  A path traced by a moving point under given condition(s) is called a locus.  e.g. move point P such that  APB remains unchanged. What is the locus of P?

6. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems What is the restriction of each drawing device shown on the left? Drawing Devices

7. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Collinear Points (I) Are points A, B and P collinear? If slope of AP  slope of PB, then A, P and B are collinear. ∵ Slope of AB , slope of BP  1 ∴ A, P and B are not collinear.

8. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Collinear Points (II) Are points A, B and P collinear? If slope of AP  slope of PB, then A, P and B are collinear. ∵ Slope of AB  0.5, slope of BP  0.5 ∴ A, P and B are collinear.

9. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems If P(x, y) is a moving point such that slope of BP equals slope of AB, what is the locus of P? How to find an equation connecting x and y? ∵ slope of AB  slope of BP ∴ P lies on the straight line which passes through A and B. Equations of Straight Lines ∵ slope of AB  0.5 and slope of BP  ∴ 0.5  i.e.x  2y  2  0 This kind of equation is called the equation of a straight line.

10. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems  General form of a straight line: Ax  By  C  0 where A and B are not both zero.  Slope   x -intercept   y -intercept = General Form of Straight Lines

11. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems  If L 1 // L 2, then m 1  m 2.  If m 1  m 2, then L 1 // L 2.  If L 1  L 2, then m 1  m 2  1 。  If m 1  m 2  1, then L 1  L 2 。 General Form of Straight Lines

12. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Locus of the Tip What is the locus of the tip of the minute-hand? The locus is a circle!

13. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Equations of Circles OP  4 If the coordinates of the tip P of minute-hand are (x, y), what is the equation connecting x and y?

14. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems Equations of Circles x 2  y 2  4 2 OP  4

15. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 10 Coordinate Treatment of Simple Locus Problems  The standard form of a circle with centre (h, k) and radius r: (x  h) 2  (y  k) 2  r 2  The general form of a circle x 2  y 2  Dx  Ey  F  0  By completing the square, Equations of Circles

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