Transformations

Question 1

Transformation (definition)

Answer 1

A one-to-one function that maps a point in the plane to a point in the plane

Question 2

Preimage (definition)

Answer 2

The original point/image

Question 3

Image (definition)

Answer 3

The transformed point/image

Question 4

Reflection (definition)

Answer 4

Any point, P, NOT on the line of reflection onto the point P’ so that the line of reflection is the PERPENDICULAR BISECTOR of the segment connecting P and P’

Question 5

What does r with a subscript of y=4 represent?

Answer 5

A reflection across the line of y=4

Question 6

What does r with subscript l: P —> P’ represent?

Answer 6

A reflection across line l that maps point P to P’

Question 7

What does r with subscript l (P) = P’ represent?

Answer 7

The image of P under a reflection in line l is P prime

Question 8

What does P with r with subscript l above —> leading to P’ represent?

Answer 8

The image of P under a reflection in line l is P prime.

Question 9

What is a translation?

Answer 9

A transformation of the plane that maps each point to a point in the same direction at the same distance.

Question 10

What does T with subscript a,b times and (P) = P’ represent?

Answer 10

The translation of P a spaces left or right and b spaces up or down is equal to P prime

Question 11

What is a reflection (with fixed point P)?

Answer 11

Any point that maps to its prime point where P is the midpoint of the segment

Question 12

Point reflection in the origin (formula)

Answer 12

(x, y) with R(0,0) —> (-x, -y)

Question 13

Point reflection formula for any point

Answer 13

(x, y) with R(m,n) —> (2m-x, 2n-y)

Question 14

What properties are preserved in TRANSFORMATIONS

Answer 14

length (distance), area, parallelism, midpoint, angle measure, collinearity

Question 15

Rule for a 90 degrees clockwise rotation (along origin)

Answer 15

(x,y) —> (-y,x)

Question 16

rule for a 180 degree rotation

Answer 16

(x, y) —> (-x, -y)

Question 17

Rotation rule for 270 degree clockwise rotation

Answer 17

(x, y) —> (y, -x)

Question 18

When is a line its own image in a dilation?

Answer 18

When its center of dilation is on the line

Question 19

What do you do if the center of dilation is not on a line?

Answer 19

• The slope remains the same
• The y-intercept is multiplied by the scale factor

Question 20

What properties are persevered in dilations?

Answer 20

Angle measures, parallelism, collinearity, midpoint

Question 21

What properties are not preserved under a dilation?

Answer 21

area and distance

Question 22

How do you show two polygons are similar?

Answer 22

• if the ratio of their perimeters is equal to the scale factor AND
• if the ratio of their areas equals the square of the scale factor

Question 23

How is perimeter or circumference affected by scale factor?

Answer 23

The perimeter/circumference is multiplied by the scale factor

Question 24

How is area affect by scale factor?

Answer 24

The area is multiplied by the scale factor squared