Coordinate Geometry I

1. Y-axis Q(x2,y2) y2 y1 P(x1,y1) X-axis 0 x2 x1 Coordinate Geometry I YOU NEED TO KOWN THE FORMULAE ! BASIC Point Formulas Distance, Midpoint, Gradient By Mr Porter

2. (x2, y2) (x1, y1) B(5,7) 10 4 A(1,-3) The exact distance between A(1, -3) and B(5, 7) is Distance between 2 Points P(x1, y1) and Q(x2, y2) Example 1: Find the distance between A(1,-3) and B(5,7). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula : YOU NEED TO KOWN THE FORMULA ! 2) Show substitution into formula clearly. Use calculator to evaluate (5-1)2 + (7--3)2 Simplify the surd.

3. (x2, y2) (x1, y1) P(-3, 5) 8 10 Q(5,-5) Example 2: Find the distance between P(-3,5) and Q(5,-5). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula : 2) Show substitution into formula clearly. YOU NEED TO KOWN THE FORMULA ! Use calculator to evaluate (5--3)2 + (-5-5)2 Simplify the surd. The exact distance between P(-3, 5) and B(5, -5) is

4. (x2, y2) (x1, y1) B(5,7) 10 4 A(1,-3) Mid-Point of 2 Points P(x1, y1) and Q(x2, y2) Example 1: Find the Mid-Point of A(1,-3) and B(5,7). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula: (average point / co-ordinates) YOU NEED TO KOWN THE FORMULA ! 2) Show substitution into formula clearly. The mid-point of A(1, -3) and B(5, 7) is (3, 2).

5. (x2, y2) (x1, y1) P(-3, 5) 8 10 Q(5,-5) Example 2: Find the mid-point of P(-3,5) and Q(5,-5). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula : YOU NEED TO KOWN THE FORMULA ! 2) Show substitution into formula clearly. The mid-point of P(-3,5) and Q(5,-5) is (1, 0).

6. (x2, y2) (x1, y1) B(5,7) 10  4 Always try to write the gradient, m, as a simplified IMPROPER fraction A(1,-3) The gradient of the line passing through A(1,-3) and B(5,7) is : Gradient, m, of line joining 2 Points P(x1, y1) and Q(x2, y2) Example 1: Find the gradient, m, of the line passing through points A(1,-3) and B(5,7). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula : YOU NEED TO KOWN THE FORMULA ! 2) Show substitution into formula clearly.

7. (x2, y2) (x1, y1) P(-3, 5) 8  10 Q(5,-5) Always try to write the gradient, m, as a simplified IMPROPER fraction The gradient of the line passing through P(-3,5) and Q(5,-5) is : Example 2: Find the gradient, m, of the line passing through points P(-3,5) and Q(5,-5). Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. 1) Formula : YOU NEED TO KOWN THE FORMULA ! 2) Show substitution into formula clearly.

8. (x2, y2) (x1, y1) Simplify all surds! The distance AB is d = A(-3,7) B(5,1) The mid-point C is (1,4) The gradient of line AB is Exercise 1) Given the two points A(-3,7) and B(5,1) find the a) distance AB b) point C, the mid-point of interval AB c) gradient, mAB, of the line joining AB Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. YOU NEED TO KOWN THE FORMULAE !

9. (x2, y2) (x1, y1) The distance PQ is d = Q(6,4) The gradient of line PQ is P(-5,-3) The mid-point R is Exercise 2) Given the two points P(-5,-3) and Q(6,4) find the a) distance PQ b) point R, the mid-point of interval PQ c) gradient, mPQ, of the line joining PQ Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. YOU NEED TO KOWN THE FORMULAE !

10. (x1, y1) (x2, y2) The distance LM is d = M(-1,5) The gradient of line LM is L(8,-3) The mid-point K is Exercise 3) Given the two points L(8,-3) and M(-1,5) find the a) distance LM b) point K, the mid-point of interval LM c) gradient, mLM, of the line joining LM Helpful Hints: It is usually a good idea to make a little sketch. Write down ALL point formulae used in coordinate geometry. Label points clearly (x1, y1) & (x2,y2) Is your answer what you expect or realistic for the problem. YOU NEED TO KOWN THE FORMULAE !

11. FORMULAE TEST Given the two points P(x1,y1) and Q(x2,y2)., write down the formula for: a) Distance PQ b) Mid-point of the interval PQ c) Gradient of the interval PQ. YOU NEED TO KOWN THE FORMULAE ! These will be revised again in HSC application type questions.