Lesson 5- Geometry & Lines Objectives : Quick recap on last weeks work Coordinate geometry definitions - Equations of straight lines - Intersection of lines (Simultaneous equations) Intersection of line and quadratic (solve by algebra) Intersection of line and quadratic (solve by graph) Some types of curve 6 December, 2018 INTO - Foundation L5 MH

Recap what we did last week We quickly talked about: Accuracy of numbers as defined by: Decimal Places (dp) or Significant Differences (sf) Irrational or Rational numbers Rational numbers can be expressed as a fraction in its lowest for iii. Rules of Indices 6 December, 2018 INTO - Foundation L5 MH

Some definitions Circumference Radius Diameter Collinear – points lie on a straight line Parallel – going in the same direction Quadrilateral – a shape with 4 sides Triangle - a shape with 3 sides Right angle - 90º Right-angled triangle Isosceles triangle – 2 sides the same length Equilateral triangle – all sides the same length Scalene triangle – all sides different lengths Trapezium – 2 parallel sides Parallelogram – pairs of parallel sides Rhombus – parallelogram with all sides equal Square –4 sides equal, all angles 90º Rectangle – 4 sides, all angles 90º Vertex, vertices – corner, corners Diagonal – line joining opposite corners Circumference Radius Diameter 6 December, 2018 INTO - Foundation L5 MH

Definitions Gradient Midpoint Length Perpendicular Perpendicular Bisector 6 December, 2018 INTO - Foundation L5 MH

Gradient A(3,5) ∆y B(0,2) ∆x 6 December, 2018 INTO - Foundation L5 MH

Midpoint of a line P(-10,8) dy Mid = (0,1) Q(10,-6) dx 6 December, 2018 INTO - Foundation L5 MH

Length of line P(-10,8) dy Q(10,-6) dx 6 December, 2018 INTO - Foundation L5 MH

Perpendicular Lines Let Gradient line1 = m1 Gradient line2 = m2 m1×m2 = -1 m2=-1/2 m1=2 m2 = -1/m1 6 December, 2018 INTO - Foundation L5 MH

Perpendicular Bisector Find Midpoint Find grad1 Find grad2 Plot line P(4,8) Q(-4,-8) 6 December, 2018 INTO - Foundation L5 MH

m gives the gradient of the line and c gives the y intercept. 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c dy = 2 dx = 1 y = 2x + 3 y intercept = 3 The gradient is defined as the dy/dx

m gives the gradient of the line and c gives the y intercept. 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c dy = 3 y = 3x - 4 dx = 1 The gradient is defined as the dy/dx y intercept = -4

m gives the gradient of the line and c gives the y intercept. 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c y = ½x + 1 dy = 1 dx = 2 y intercept = 1 The gradient is defined as the dy/dx

Consider the straight lines shown below: Can you split the lines into two groups based on their gradients ? Positive gradient Lines (a) (c) and (d) slope upwards from left to right. Negative gradient Lines (b) and (e) slope downwards from left to right.

m gives the gradient of the line and c gives the y intercept. 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c y intercept = 3 dy = 4 dx = 5 The gradient is defined as the dy/dx

Determine the equations of the following lines 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Determine the equations of the following lines y = 2x + 3 y = 3x – 5 y = -x + 6 Y = ½x –2 Y = - 4x –9 y = ¾x

Find equation of straight line Given points A(3,4) , B(-6,2) Find gradient (m) Find the equation of the line through AB

Point of Intersection Find the intersection point between the lines : y = 2x+3 y = -2x+1 C Answer C( -1/2 , 2 ) 6 December, 2018 INTO - Foundation L5 MH

Points of Intersection Find the intersection point between the curve and the line : y = x2-2x-3 y = 2x-1 B Answer A(2-√6 , 3-2√6) B(2+√6, 3+2√6) A 6 December, 2018 INTO - Foundation L5 MH

Progress ? Objectives : Quick recap on last lesson work Coordinate geometry definitions - Equations of straight lines - Intersection of lines (Simultaneous equations) Intersection of line and quadratic (solve by algebra) Intersection of line and quadratic (solve by graph) Some types of curve (**) 6 December, 2018 INTO - Foundation L5 MH

Challenge Question The line with equation 5x + y = 20 meets the x-axis at A and the line with equation x + 2y = 22 meets the y axis at B. The two lines intersect (meet, cross) at point C. sketch the two lines on the same diagram calculate the co-ordinates of A, B, C calculate the area of triangle OBC where O is the origin find the coordinates of point E such that ABEC is a parallelogram 6 December, 2018 INTO - Foundation L5 MH

Point C, solve simultaneously B(0,11) C(Solve) C B O A Point C, solve simultaneously Area of OBC is 11 square units C(2,10) 6 December, 2018 INTO - Foundation L5 MH

find the coordinates of point E such that ABEC is a parallelogram 6 December, 2018 INTO - Foundation L5 MH

3 basic curve types 6 December, 2018 INTO - Foundation L5 MH