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### Sec 3 E Maths Notes Coordinate Geometry

• 1. 4048 3EM Coordinate Geometry (1) Math Academy® © All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or stored in any retrieval system of any nature without prior permission. © www.MathAcademy.sg 1 Be a lifelong student. The more you learn, the more you earn and more self confidence you will have. - Brian Tracy Notes: Coordinate Geometry [A] Distance Formula This formula is an application of Pythagoras' theorem for right triangles: Note that the distance is taken to be positive. Example 1: Given that is an isosceles triangle with vertices , and and , find the value of . Ans: Solution: ABC ( , 1)A p - (2, 5)B (3, 4)C ACAB = p 3- ACAB = Given two points and , the distance between these points is given by the formula: ( )1 1,x y ( )2 2,x y 2 21 2 21 )()( yyxxPQ -+-= Length same, apply distance formula
• 2. 4048 3EM Coordinate Geometry (1) Math Academy® © All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or stored in any retrieval system of any nature without prior permission. © www.MathAcademy.sg 2 Example 2: In the diagram below, is a regular hexagon. , and has coordinates , and respectively. (i) State the coordinates of , in terms of . [1] (ii) Justify, showing all workings clearly, why the coordinate of will not be an integer. [2] Solution: (i) (ii) Let the midpoint of be . By Pythagoras theorem, Since 12 is not a perfect square, the coordinate of will not be an integer. Or can apply distance formula to and , whereby . ABCDEF A E F (0,6) ( , 0)s (0,2) B s x - D ( , 8)B s DF X 2 2 2 2 4s + = 12s = 2 12DF = x - D (2 , 2)D s ( , 0)E s 4DE =
• 3. 4048 3EM Coordinate Geometry (1) Math Academy® © All rights reserved. No part of this document may be reproduced or transmitted in any form or by any means, or stored in any retrieval system of any nature without prior permission. © www.MathAcademy.sg 3 Example 6: Given that the gradient of and is , find the possible coordinates of . Ans: Solution: Example 7: The diagram, which is not drawn to scale, shows the three lines , and . (a) Find the coordinates of , and . [4] (b) The point is the same distance from as it is from Find the value of . [1] Ans: (a) (b) 0.5 (3, )A p- 2 ( , )B p p- 2 1 - B ( 1,1), (1.5,2.25)B B- 2 ( ) 1 3 2 p p p - - = - - - 5=y xy -= 3 343 += xy A B C ( ,0)k A B k 6 1 ( 2,5), (3,5), ( ,2 ) 7 7 A B C- Casio mode 3, 3 y x O A B C horizontal Positive gradient Negative gradient