1 / 23

Lesson 5- Geometry & Lines

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)

wbook
Download Presentation

Lesson 5- Geometry & Lines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 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 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 INTO - Foundation L5 MH

  4. Definitions • Gradient • Midpoint • Length • Perpendicular • Perpendicular Bisector INTO - Foundation L5 MH

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

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

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

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

  10. Straight Line Graphs y 10 9 8 All straight line graphs are of the form y = mx + c 7 6 5 4 3 y intercept = 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 m gives the gradient of the line and c gives the y intercept. dy= 2 dx= 1 y = 2x + 3 The gradient is defined as the dy/dx

  11. Straight Line Graphs y 10 9 8 All straight line graphs are of the form y = mx + c 7 6 5 4 3 y intercept = -4 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 m gives the gradient of the line and c gives the y intercept. dy= 3 y = 3x - 4 dx= 1 The gradient is defined as the dy/dx

  12. Straight Line Graphs y 10 9 8 All straight line graphs are of the form y = mx + c 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 y intercept = 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 m gives the gradient of the line and c gives the y intercept. y = ½x + 1 dy= 1 dx= 2 The gradient is defined as the dy/dx

  13. (b) (d) (a) (c) (e) 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. Straight Line Graphs y 10 9 8 All straight line graphs are of the form y = mx + c 7 y intercept = 3 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 m gives the gradient of the line and c gives the y intercept. dy= 4 dx= 5 The gradient is defined as the dy/dx

  15. y Determine the equations of the following lines 10 9 1 5 8 7 6 5 2 4 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 6 -4 -5 3 -6 -7 -8 -9 -10 • 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 ) 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 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 (**) 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 INTO - Foundation L5 MH

  21. A(4,0) B(0,11) C(Solve) C B O A Point C, solve simultaneously Area of OBC is 11 square units C(2,10) INTO - Foundation L5 MH

  22. find the coordinates of point E such that ABEC is a parallelogram E C(2,10) E B(0,11) C B A(4,0) A E(-2,21) INTO - Foundation L5 MH

  23. 3 basic curve types INTO - Foundation L5 MH

More Related