Co Ordinate Geometry

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# Co Ordinate Geometry - PowerPoint PPT Presentation

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). Co Ordinate Geometry.

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Presentation Transcript
Midpoint of a Line Segment

Distance

Parallel lines

Perpendicular lines

Equation of a line

Two points

Intersection of two straight lines

Terms for excellence

Rural Neighbours

Goat fences

Game park (2006 SINCOS)

Co Ordinate Geometry

L2 Coordinate Geometry

M.Guttormson

Midpoint of a Line Segment

L2 Coordinate Geometry

M.Guttormson

Distance

L2 Coordinate Geometry

M.Guttormson

L2 Coordinate Geometry

M.Guttormson

Parallel lines

L2 Coordinate Geometry

M.Guttormson

Perpendicular lines

L2 Coordinate Geometry

M.Guttormson

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

L2 Coordinate Geometry

M.Guttormson

Equation of a line (Point and gradient)

L2 Coordinate Geometry

M.Guttormson

Intersection of two straight lines

L2 Coordinate Geometry

M.Guttormson

Terms for excellence

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

L2 Coordinate Geometry

M.Guttormson

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

L2 Coordinate Geometry

M.Guttormson

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?

L2 Coordinate Geometry

M.Guttormson

Game park

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.

L2 Coordinate Geometry

M.Guttormson

Game park

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.

L2 Coordinate Geometry

M.Guttormson