Co-ordinate Geometry Achievement Standard 2.5. The Co-ordinate Plane x y A B C (-4,4) (6,2) (-3,-2)

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Presentation transcript:

Co-ordinate Geometry Achievement Standard 2.5

The Co-ordinate Plane x y A B C (-4,4) (6,2) (-3,-2)

Distance Between 2 Points x y A B (-4,4) (6,2) a b c a 2 + b 2 = c 2 Problems

1)Find the length of AC 2)Find the length of CD 3)ACE makes a triangle, Find the length of each side to show that it’s Scalene. 4)Show that CEF is an Isosceles Triangle. 5)Find the length of a line from (-3,-2) to (4,-1) 6*)Use Pythagoras to show that CBE is a right angled triangle. Page 129 ex16.2 Q2 onwards Distance Between 2 Points x y F E D C B A

Midpoint of 2 Points x y A B (-4,4) (6,2) -4+6, ( ) = (1, 3) Average ‘x’Average ‘y’

1)Find the midpoint of BE 2)Find the midpoint of AF 3)If DK is a straight line and C is the midpoint, What are the co-ordinates of K? 4)Show that E is the midpoint of BF. Page 127, ex 16.1 Midpoint of 2 Points x y F E D C B A

Gradient Between 2 Points x y A B (-4,4) (6,2) run rise Gradient = rise run Page 130 ex 16.3

Equation of a line x y C (-3,-2) Needs 2 things Gradient (Slope) = m Point on the line = (x 1, y 1 ) y - y 1 = m (x - x 1 ) 5 4 Page 134 ex 16.7 Page 135 ex 16.8 Page 136 ex16.10

Perpendicular line x y A (0,2) Needs 3 things Gradient (Slope of first line) = m Gradient of Perp. Line = m┴ Point on the line = (x 1, y 1 ) y - y 1 = m┴ (x - x 1 ) Y = 5/4 x BpBp (4,-2) Perpendicular slope is always -1/m Page 138 ex 16.11

Achieved Problems Distance between 2 points Midpoint of a line Equation of a line Equation of a parallel line

Merit problems Perpendicular Bisector Intersection of 2 lines Altitude of a triangle Median of a triangle