Inductive Reasoning
The definition of inductive reasoning is...
using logic when using a specific example to make a general rule
Any change to the size, orientation, or location of a geometric object
Transformation
When looking at rotations, rotating an object we use the circle. How many degrees is a full circle for when objects are rotated?
360 degrees
When reflecting an image the new geometric image appears....
backwards or opposite
Does a translation change the orientation of a geometric object?
No
Definition of conjecture:
educated guess, where no evidence is needed.
A transformation where the geometric object is turned either clockwise or counter clockwise, and the orientation is changed.
Rotation
What are the two ways you can rotate a geometric object
CW - Clockwise
CCW - Counter clockwise
Point A is on coordinate plane at (5,-6) if it is reflected across the X axis what is the new coordinates?
A' (5,6)
What is the directions for moving or translating an object called?
vector
What is the next number in the sequence: 5, 15, 45
135 (times 3)
A transformation where a geometric object is flipped across a certain axis. Orientation maybe changed.
Reflection
If point B sits at the coordinates (2,2) in quadrant 1, and it is rotated to coordinates (-2,-2) which quadrant is it in now?
Quadrant 3
If a square and all its points are in quadrant 3, and it is reflected across the y-axis, it is now in quadrant....
Quadrant 4
Point A is at (5,5) and is translated a vector of <4,-4> what are the new coordinates?
What is the next number in this sequence: 2,4,8,14....
22 (adding 2 more than the previous numbers)
A transformation where the a geometric figure is moved or slid to a new location by a vector. Orientation is preserved.
Translation
If line segment AB is on the coordinate plane A is located at (-3,2) and B is at (-6, 2) what are the new coordinates after it is rotated 90 degrees clockwise.
A' (2,3) B'(2,6)
If line line XY is on a coordinate plane and point X is at (1,2) and point Y is at (-2,2). What is the new location after a reflection of y=x.
X' (2,1)
Y' (2,-2)
Point Z starts at (2,-3) and is moved to (-1,-5) what is the vector?
<-3, -2>
Make a conjecture based on these expressions:
1 + 3 = 4
7 + 9 = 16
5 + 15 = 20
The sum of two odd numbers equals an even number
The original geometric figure in a transformation is known as the ____________ (before), and the new geometric figure is know as the ____________ (after)
preimage, image
Triangle ABC is on the coordinate plane, point A is at (1,1) point B is (3,3) and point C is (5,1). What are the new coordinates if the triangle is rotated 270 degrees counter clockwise?
A' (1,-1)
B' (3, -3)
C'(1,-5)
Point Z is on a coordinate plane at (-9,8). If it is reflected across the y=-x what is the new coordinates?
Z' (-8,9)
Triangle ABC is translated by of vector <-6,5> describe the movement:
6 spaces left
5 spaces up