2 D Geometry Cartesian Coordinate system yaxis xaxis

2 -D Geometry

Cartesian Coordinate system y-axis x-axis

y-axis Quadrant II Quadrant I Origin Quadrant III Quadrant IV xaxis

All points on a graph are plotted by first finding the x-coordinate and then the y-coordinate You always graph a point starting from the Origin All points are written in the form ( x, y )

Quadrant II Quadrant I x is negative x is positive y is positive Quadrant III Quadrant IV x is negative x is positive y is negative

y V E R T I C A L First we look at how far ACROSS the grid the point is, this is on the horizontal axis. 4 3 2 1 0 1 2 3 4 HORIZONTAL 5 Then we look at how far up the point is, this is on the vertical axis. x

y V E R T I C A L We write the numbers with the horizontal number first: 4 3 2 1 0 1 2 3 HORIZONTAL 4 5 We separate the numbers with a comma. x

y V E R T I C A L 4 3 2 1 0 1 2 3 HORIZONTAL 4 5 We put brackets around the coordinates. x

Point (3, 5)

Rigid Transformations that do not change shape or size. n Pre-image is the original shape n Image is the shape that undergoes a transformation n

NOTATION The original figure is named as we have learned so far. For instance a point would be called A. This is the preimage. n The image of point A is called A’ (said, “A prime”). This is so we can tell the difference between the 2 identical figures. n

Transformations There are 3 types of rigid transformations: § Translation – shapes slide § Rotation – shapes turn § Reflection – shapes flip

Translation n Shapes slide – Every point of a figure moves in a straight line, all points move the same distance and same direction.

Rotation n Rotations turn – Every point of a figure moves around a given point called the center of rotation.

Reflection n Reflections flip. – In a reflection, a line plays the role of a mirror. Every point in a figure is ‘flipped’ across the line.

Summary n What is the movement of a rotation? – What does is ‘turn’ around? n What is the movement of a translation? – What does it ‘slide’ on? n What is the movement of a reflection? – What does it ‘flip’ over? n n n When can the pre-image and the image be a different size? How do you notate the pre-image? (For instance segment AB) How do you notate the image?

Perpendicular line Construction Perpendicular Bisector Aim: Divide a line in half at 90º P Perpendicular Line from a point NEAR a line Perpendicular Line from a point ON a line P

Perpendicular Bisector A Aim: Divide a line in half at 90º Rule a line (leaving some space on each side of the line) Click to start Step 1 Home

Perpendicular Bisector A Aim: Divide a line in half at 90º Compass point Set your compass to about ¾ of the line length Step 1 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Set your compass to about ¾ of the line length Step 1 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Set your compass to about ¾ of the line length Step 1 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step Arc into space each side of the line Hom

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step 1 Arc into space each side of the line Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step Arc into space each side of the line Hom

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step 1 Arc into space each side of the line Home

Perpendicular Bisector Aim: Divide a line in half at 90º Compass point Step 1 Arc into space each side of the line Home

Perpendicular Bisector B Aim: Divide a line in half at 90º Keep the compass the same Arc into space each side of the line Step 1 Step 2 Compass point Home

Perpendicular Bisector Aim: Divide a line in half at 90º Keep the compass the same Arc into space each side of the line Step Compass point Hom

Perpendicular Bisector Aim: Divide a line in half at 90º Keep the compass the same Arc into space each side of the line Step Compass point Hom

Perpendicular Bisector Aim: Divide a line in half at 90º Arc into space each side of the line Step 1 Step 2 Compass point Home

Perpendicular Bisector C Aim: Divide a line in half at 90º Use a ruler to join this point With this point Step 1 Step 2 Step 3 Home

Perpendicular Bisector Aim: Divide a line in half at 90º Perpendicular bisector This should be 90º 1 2 And half way Step 1 Step 2 Step 3 The End Home

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point near a line P Rule a line Mark a point near the line (about 4 cm away is fine) Leave some space on either side of the line Step Click to start Hom

Perpendicular Line from a Point A Aim: Construct a line at 90º through a point near a line Compass point P Set your compass to reach over the line so the arc will cut twice Step Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Set your compass to reach over the line so the arc will cut twice Step Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Move your compass to one side Step Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Step Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Step Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line Compass point P Step Hom

Perpendicular Line from a Point B Aim: Construct a line at 90º through a point near a line P Step 1 Step 2 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Step 1 Step 2 Keep the compass the same Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Keep the compass the same Arc into space each side of the line Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Keep the compass the same Arc into space each side of the line Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Arc into space each side of the line Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Arc into space each side of the line Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Step 1 Step 2 Arc into space each side of the line Home

Perpendicular Line from a Point C Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Keep the compass the same Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Keep the compass the same Step 3 Home

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Keep the compass the same Step 3 Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line P Compass point Arc into space each side of the line Step 1 Step 2 Step 3 Home

Perpendicular Line from a Point D Aim: Construct a line at 90º through a point near a line Use a ruler to join this point P With this point Step Hom

Perpendicular Line from a Point Aim: Construct a line at 90º through a point near a line This should be 90º Perpendicular Line P 90º Step 1 Step 2 Step 3 The End Home

Construct the bisector of an angle n n n Draw the angle aob. Using the vertex o as centre draw an arc to meet the arms of the angle at x and y. Using x as centre and the same radius draw a new arc. Using y as centre and the same radius draw an overlapping arc. Mark the point where the arcs meet. The bisector is the line from o to this point. a x o x x y b