The document discusses key concepts in coordinate geometry, including: 1) How to calculate the distance between two points using their coordinates. The distance formula is given as the square root of the sum of the squared differences between the x- and y-coordinates. 2) How to find the midpoint between two points by taking the average of their x- and y-coordinates. The midpoint formula is given. 3) How to find a point that divides a line segment between two end points in a given ratio of distances, using a formula that involves the x- and y-coordinates and the ratio. Examples of each concept are worked out.

1. MATHEMATICS TOPIC : COORDINATE GEOMETRY Presented by : UMI KALSOM BINTI ABDOL RAHAMAN 870728-04-5308

2. Distance Mid-Point Point dividing segment with ratio m:n GEOMETRY COORDINATE

3. General Information General Equation for straight line y = mx + c Gradient, m = y 2 -y 1 x 2 -x 1 2 Parallel straight line have same gradient 2 lines perpendicular, m 1 m 2 = -1

4. GEOMETRY COORDINATE a) Distance How to find the distance between two point B (x 2 ,y 2 ) A (x 1 ,y 1 ) Line AB = (X 1 - X 2 ) 2 + (Y 1 - Y 2 ) 2

5. Example 1 Given P(3,2), Q(7,5), find the distance between point P and Q. Answer : Let (x 1 ,y 1 ) = (7,5) and (x 2 ,y 2 )= (3,2) PQ = (X 1 - X 2 ) 2 + (Y 1 - Y 2 ) 2 = (7-3)² + (5-2)² = 4² + 3² = 5 unit Q (7,5) P (3,2)

6. GEOMETRY COORDINATE b) Mid-Point How to find the midpoint of two points R = midpoint B (x 2 ,y 2 ) A (x 1 ,y 1 ) Mid Point = x 1 + x 2 , y 1 + y 2 2 2 R

7. Example 2 Find the midpoint coordinates for AB lines A( 5,7) B( 3,-1) Answer: = 5+3 7 + (-1) 2 2 = ( 4 , 3 ) AB = x 1 + x 2 , y 1 + y 2 2 2 B (3,-1) A (5,7)

8. Example 3 Given M ( a , -3), N (-4, b ) and the midpoint is (3,-2), find the value of a and b Answer : PQ = a + (-4) , -3 + b 2 2 a – 4 = 3 -3 + b = -2 2 2 a = 10 b = -1

9. c) Point that internally divides a line segment in the ratio m:n GEOMETRY COORDINATE P (X 1 , Y 1 ) Q (X 2 , Y 2 ) n m R (a,b) a = nx 1 + mx 2 , b = ny 1 + my 2 m+n m+n

10. Example 4 P is a point that located in the straight line AB which A( 2,6) and B(8,0) with ratio AP: 2PB. Find the coordinate of P. Answer : AP : 2PB A (2,6) B (8,0) P 2 1 a = nx 1 + mx 2 , b = ny 1 + my 2 m+n m+n P = 1 x 2 + 2 x 8 , 1x6 + 2 x 0 2 + 1 2 + 1 = (6 , 2 ) So, coordinate P is (6,2).

11. Review DISTANCE Line AB = (X 1 - X 2 ) 2 + (Y 1 - Y 2 ) 2 RATIO m:n a = nx 1 + mx 2 , b = ny 1 + my 2 m+n m+n Mid Point = x 1 + x 2 , y 1 + y 2 2 2

12. Exercise Find distance between the two points given: A(-1,2),B(2,6) G(4,-3), H( -5,-3) C(15,4) , E(3,-1) 2. Find the midpoint of S(10,-3) and T(-4,-1) straight line. 3. Find the ratio point P(3,4) that divide straight line AB, A(-1,2) and B(9,7).

13. Thank You…