Unit 5 Test prep Flashcards
Reflection X axis
(X-y)
Reflection y axis
(-X, y)
Reflection y=x
(Y,X)
Reflection y=-x
(-y,-x)
Reflection x=c (any vert line)
(2C-x,y)
Rotation 90 counterclockwise
(-y,x)
When doing a rotation, the SHAPE rotates in the direction stated (cc or cw) NOT the paper, if doing the paper trick, go the opposite direction (cc or cw)
Rotation 180 counterclockwise
(-x,-y)
When doing a rotation, the SHAPE rotates in the direction stated (cc or cw) NOT the paper, if doing the paper trick, go the opposite direction (cc or cw)
Rotation 270 counterclockwise
(Y,-X)
When doing a rotation, the SHAPE rotates in the direction stated (cc or cw) NOT the paper, if doing the paper trick, go the opposite direction (cc or cw)
What is an isometry?
An isometry is a transformation that preserves the shape and distance of a figure
What is a direct isometry?
An isometry that preserves orientation
What is an opposite isometry?
An isometry that does NOT preserve orientation
How can you prove that two triangles are congruent?
The angle measures and distance will be the same if congruent
What do you always need to have with the rotation or dilation transformations
You need to have “about the origin” or “about (0,0)”
How to do a dilation from point in center of shape (2)
- Measure distance from center point to point of shape, place compass on edge of point, make a little notch to mark new point
- Repeat for every point
- Draw and connect
How to do dilation of 3 from center point inside shape
- Measure distance from center point to outer point of shape, place compass on outer point of shape, make notch
- Place compass on notch and make another using the same distance
- Draw and connect
How to dilate from point on the shape (2)
- Measure distance from one point to another ex. A to B, then put compass on other point, make a mark for the new point
- Repeat on other points
- Draw and connect
How to construct a line of reflection
- Draw a line from one of the points to the corresponding point on the other shape ex. A to A
- Put compass on endpoint of one side, measure more than half the distance of line (exact distance doesn’t matter) then draw a curve
- Repeat for other endpoint with same distance
- Use intersection points to draw line of reflection
How to translate shapes
- Measure distance of translation arrow (usually called AB)
2 put compass on each point of shape and draw a curve - Measure distance from a point on the shape to the closer point on the translation arrow (ex. T to A, T is part of shape)
- Place compass on B and draw arc so it intersects with the previous curve near the same point once
- Repeat step 4 for all other points
- Draw and connect
How to reflect a shape
- Measure from a point to any place over the line of reflection and draw curve that hits line of reflection twice
- On the arc just drawn place compass on intersection point with the same distance set, and draw another arc, do the same for other intersection point
- Repeat steps 1&2 for other points
- Draw and connect
Exterior angle measure formula
360 divided by the number of sides on shape
Ex. Hexagon
360/6
=60
So each exterior angle is 60 degrees
How to solve line equation problems
Example 1: The line y=4x+3 is dilated by a scale factor of 2 centered at the point (3,15) What is the equation of the image?
- Plug in points to equation
(15)=4(3)+3 gives you 15=15 which means the answer is the same line: y=4x+3 - If the answer is not the same line multiply the given coordinates by the scale factor
How to do a rotation construction (60 degrees)
- Place compass on given point, measure to a point on the shape,(ex D) draw a large arc
- Place compass on point first measured to (ex D), with same distance draw another arc that intersects with first arc
- Repeat for all other points
- Draw and connect
How to do a rotation 120 degrees
- Place compass on given point, measure to a point on the shape,(ex D) draw a large arc
- Place compass on point first measured to (ex D), with same distance draw another arc that intersects with first arc
- Now move compass to 2nd drawn arc, with same distance draw another arc that intersects with 1st arc, that intersection point is the new point
- Repeat for all other points
- Draw and connect
