1. Coordinate Geometry I BASIC Point Formulas Distance, Midpoint, Gradient By Mr Porter YOU NEED TO KOWN THE FORMULAE ! 0 x1x1 x2x2 y2y2 y1y1 P(x 1,y 1 ) Q(x 2,y 2 ) Y-axis X-axis

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

3. Example 2: Find the distance between P(-3,5) and Q(5,-5). Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. P(-3, 5) Q(5,-5) 10 8 1) Formula : (x 1, y 1 ) (x 2, y 2 ) 2) Show substitution into formula clearly. 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 YOU NEED TO KOWN THE FORMULA !

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

5. Example 2: Find the mid-point of P(-3,5) and Q(5,-5). Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. P(-3, 5) Q(5,-5) 10 8 1) Formula : (x 1, y 1 ) (x 2, y 2 ) 2) Show substitution into formula clearly. The mid-point of P(-3,5) and Q(5,-5) is (1, 0). YOU NEED TO KOWN THE FORMULA !

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

7. Example 2: Find the gradient, m, of the line passing through points P(-3,5) and Q(5,-5). Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. (x 1, y 1 ) (x 2, y 2 ) 1) Formula : 2) Show substitution into formula clearly. 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 : P(-3, 5) Q(5,-5) 10 8  YOU NEED TO KOWN THE FORMULA !

8. 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, m AB, of the line joining AB Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. A(-3,7) B(5,1) (x 1, y 1 ) (x 2, y 2 ) Simplify all surds! The distance AB is d = The mid-point C is (1,4) The gradient of line AB is YOU NEED TO KOWN THE FORMULAE !

9. 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, m PQ, of the line joining PQ Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. P(-5,-3) Q(6,4) (x 1, y 1 ) (x 2, y 2 ) The distance PQ is d = The mid-point R is The gradient of line PQ is YOU NEED TO KOWN THE FORMULAE !

10. 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, m LM, of the line joining LM Helpful Hints: 1)It is usually a good idea to make a little sketch. 2)Write down ALL point formulae used in coordinate geometry. 3)Label points clearly (x 1, y 1 ) & (x 2,y 2 ) 4)Is your answer what you expect or realistic for the problem. M(-1,5) L(8,-3) (x 1, y 1 )(x 2, y 2 ) The distance LM is d = The mid-point K is The gradient of line LM is YOU NEED TO KOWN THE FORMULAE !

11. FORMULAE TEST Given the two points P(x 1,y 1 ) and Q(x 2,y 2 )., 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.