1. Co Ordinate Geometry Midpoint of a Line Segment Distance Gradients
Parallel lines
Perpendicular lines
Equation of a line
Two points
Point and gradient
Intersection of two straight lines
Terms for excellence
Rural Neighbours
Goat fences
Game park (2006 SINCOS)
Game Park (2006 SINCOS) Answers
Exam 2006 Questions
Exam 2006 answers
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2. Midpoint of a Line SegmentB B MP 6 3 A A 3
1.5
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3. Midpoint of a Line Segment
Exercise pages 213 (Theta)
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4. Distance B B
6.708 6 6 A A 3 3
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5. Distance Exercise 18.02 pages 215 (Theta) L2 Coordinate Geometry
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6. Gradients B B 6 A A 3
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7. Gradients Exercise 18.03 pages 216 (Theta) L2 Coordinate Geometry
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8. Parallel lines B Exercise 19.01 pages 226 (Theta)
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9. Perpendicular lines Exercise 19.02 pages 228 (Theta)
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10. Equation of a line (Two points)
The equation of a line can be expressed in the form where m is the gradient of the line and c is the y intercept.
Given two sets of coordinates, we can place them into a formula to extract the equation of the line they are on. This formula is
Use both sets of coordinates to find out the gradient
Use one set of coordinates in place of y1 and x1 along with the newly found gradient (m) to form the equation for the line.
Note that some rearranging of the formula is required to get it into the form
Exercise pages 222 (Theta)
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11. Equation of a line (Two points)B A
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12. Equation of a line (Point and gradient)
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13. Equation of a line (Point and gradient)B
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14. Intersection of two straight lines
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15. Terms for excellence Circumcenter
Collinear: Points that are on the same straight line.
Perpendicular bisector: The perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it.
Circumcenter: Three perpendicular bisectors meet in a single point called the triangles circumcenter.
Altitude: An altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side.
Orthocenter: The three altitudes of a triangle intersect in a single point, called the orthocenter of the triangle. The orthocenter lies inside the triangle.
Circumcenter
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16. Rural Neighbours
Draw a set of x and y axes that range from -8 to 8. Each value represents 1km.
As you work through the exercise mark in the points and line segments on the number plane.
1. Farmhouse A is located at (-3, 7).
Farmhouse B is located at (7,1).
Plot these points and join them with a straight line, this is a road between two houses.
b) Calculate the length of the road between farmhouse A and B.
2. Farmhouse C is located at (-3,-6). A straight road leads from it to a shop represented by point S. The shop is located midway between house A and B.
a) Show how you could calculate the coordinate for the midpoint between house A and B?
b) How far is it from the shop to the house C? (It is a road, round to 1dp)
3. What is the gradient of the line that represents road AB?
4. What is the gradient of the line that represents road CS?
5. Farmhouse D is located at (-7, -1). A straight road links house A to D. Is road AD parallel to road CS? Show valid reasons for your answer.
6. For each road create an equation in the form y= mx + c
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17. L2 Coordinate Geometry
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18. Goat Fences
Questions
1. Are the fences parallel? Explain why or why not.
2. The cost of fencing is $2.50 per metre. How much will it cost to build the two fences?
An irrigation channel EF is perpendicular (at right angles) to fence AB and passes through its midpoint.
What is the equation of the line that represents the irrigation channel
What are the coordinates where the irrigation channel and the fence CD intersect?
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19. Game park questions QUESTION ONE
(a) Calculate the distance between the points (5,-1) and (3,4).
(b) Find the equation of the line joining the points (5, -1) and (3,4).
QUESTION TWO
Find the equation of the line that is perpendicular to the line and passes through the point (6,-3).
QUESTION THREE
A large animal game park is set up on a grid system with the entrance at E (0,0) with north in the direction of the positive y-axis.
There is a lion at the point L (3,6).
The watering hole is at the point W (7,8)
(a) The lion starts walking in a straight line from its position at L towards the watering hole at point W. When it is halfway between L and W, it turns at right angles to the line LW.
Find the equation of the line the lion is now walking on, i.e. find the equation of the perpendicular bisector of the line LW.
(b) A helicopter later sights the lion at point (8,1). At this point the lion is km from a zebra that is directly east of the watering hole at W.
Find the co-ordinates of the zebra.
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20. Game park Questions QUESTION FOUR
Prove that the point A (3,5), B(7,13) and C(17,33) are collinear. Plotting points is NOT sufficient.
QUESTION FIVE
The altitudes of a triangle intersect at a point called orthocentre.
Find the coordinates of the orthocentre, O, of the triangle WXY where the vertices of the triangle are W (-3,-3), X(5,-3) and Y(1,5).
Plotting points is NOT sufficient.
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21. Game park Answers
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22. EXAM 2006 Questions
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23. EXAM 2006 Questions
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24. EXAM 2006 Questions
L2 Coordinate Geometry
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25. EXAM 2006 ANSWERS
L2 Coordinate Geometry
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26. EXAM 2006 ANSWERS
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27. EXAM 2006 ANSWERS
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28. EXAM 2006 ANSWERS
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29. EXAM 2006 ANSWERS Using midpoints Gradient Using (3, 0)
QUESTION FOUR
Using midpoints
Gradient
Using (3, 0)
Rearrange & solve
Gradient in line equation
Rearranged
Midpoints
Perpendicular Gradients
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