1. 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

2. 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

3. 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

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

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

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

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

8. 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

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

10. 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

11. 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

12. 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

13. 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.

14. 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

15. Determine the equations of the following lines1 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

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

17. 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

18. 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

19. 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

20. 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

21. 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

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

23. 3 basic curve types
6 December, 2018
INTO - Foundation L5 MH