How do you tell the difference between translation, rotation, reflection, and dilation?

Question

I need help for my math test.

Answer 1

Hey, Alexus. A translation simply moves the graph, or pre-image, without changing the size or spinning the image. So a rectangle that is 2 units wide and 4 units tall will stay that size, and will still "stand up straight" after being translated.

A reflection flips the pre-image across some line.

A rotation spins the pre-image around a point.

A dilation either expands or shrinks the pre-image. Find the difference between the coordinates of the center of dilation and the coordinates of each corner of the pre-image. Then multiply each of these differences by the scale factor.

example: to dilate the rectangle with corners at points (0,0), (1,0), (1,-2), and (0,-2) by a scale factor of 2, with a center of dilation (2,-2):
points:
(0,0) 2-0=2 and 2x2=4, 2-4=-2; -2-0=-2 and -2x2=-4, -2 - (-4)=2
SO the point (0,0) is dilated to the point (-2,2)

(1,0) is dilated to (0,2);
(1,-2) is dilated to (0,-2);
(0,-2) is dilated to (-2,-2).

Answer 2

Translation: The shape or object will move left, right, up, or down.  Also, you could have a combination like up and right.

 

Rotation: The shape or object will turn.  This is usually turning some degree clockwise or counterclockwise.

 

Reflection: The shape or object flips across a line or point

 

Dilation: The shape or object gets smaller or bigger by a scale factor.

 

I hope this helps.