State Test Review Day 8: Transformational Geometry

Name: ______Per: ______Date: ______

State Test Review Day 8: Transformational Geometry

WHAT DO YOU NEED TO KNOW?

1) A transformation is when you change an objects orientation, location, or size. There are 4 kinds of transformations.
2) A Translation is when you move an object up, down, left or right. Size and orientation do not change.
Example – Figure A has been translated to the right and up.
3) A Rotation is when you rotate a figure around a point (usually the origin). The orientation changes but not the size.

Example – Figure A has been rotated 90 degrees clockwise.
DON’T FORGET – Turn the page the given number of degrees to reveal the ANSWER!!!
4) A reflection is when a figure is reflected “over” or “in” a line of symmetry (usually the x or y-axis).

Example – Figure A has been reflected in the y - axis.
5) A dilation is when the figures points are multiplied by a scale factor to make the figure bigger or smaller. This is the only transformation that changes the figures size.
Example – If triangle ABC has coordinates A(3, 4), B(1, 0) and C(-2, 3), what will the coordinates of the new figure be after a dilation of scale factor of 3?
A’ ______B’ ______C’ ______
1) Triangle ABC has coordinates A(-5, -3), B(-5, -5) and C(-1, -5). What will the coordinates of point C beafter dilating it by a scale factor of 3?
a) C’ (-15, -3)
b) C’ (-3, -15)
c) C’ (15, -3)
d) C’ (3, 15) / 2) The point N(-6, 4) is translated to
N’(-2, -2). Which rule would describe this
translation?
a) (x, y) (x + 4, y + 6)
b) (x, y) (x - 4, y + 6)
c) (x, y) (x + 4, y - 6)
d) (x, y) (x - 4, y - 6)
3) Name the coordinates of the image of point Y(-2, 5) after it has been reflectedin the x-axis.
a) (-2, -5)
b) (2, -5)
c) (0, 5)
d) (-2, 0) / 4) The point Q(3, 4) has been translatedright 3 units and down 2 units. What are the coordinates of the image point Q’ ?
a) Q’ (0, 2)
b) Q’ (6, 6)
c) Q’ (0, 6)
d) Q’ (6, 2)
5)


a) dilation b) rotation
c) reflection d) translation
6) Which 2 figures are similar but not congruent?


a) 3 and 5 b) 1 and 3 c) 2 and 4 d) 1 and 5
7) A rectangle is plotted on the coordinate plane below. Which image shows a 90° clockwise rotation about the origin?

a) b) c) d)
8) The accompaying diagram shows a right triangle.


a)b)
c) d)
9) Gary drew a triangle on the coordinate grid shown below. If Gary reflects the triangle in the y-axis, what will be the coordinates of A’ ?
a) (1, –1)
b) (–1, –1)
c) (–1, 1)
d) (1, 1)
10) The area of triangle RST is 36 square inches. Under which transformation could the area of the image, triangle R'S'T', be greater than 36 square inches?
a) dilation
b) reflection
c) rotation
d) translation
11) One triangle is shown on the grid below. Two coordinates for a second triangle are also shown on the grid.

a) (-3, -4)
b) (-3, 5)
c) (-3, -3)
d) (-3, 7)

PART II: Extended Response

1) Rotate∆ABC 90oclockwise about the origin.
Correctly label the image points.
2) Translate figure ABCD using the rule
(x, y) (x - 6, y + 8). Label the
corresponding image points A’B’C’D’.

3) On the grid below, draw the reflection of hexagon ABCDEF in the given line.

4) Part A: On the grid below, graph and label ∆ABC with vertices A(4, 0), B(9, 0) and C(6, 4).
Part B: Translate this triangle up 5 units and to the left 2 units. Record the new points.
A’( , ) B’ ( , ) C’ ( , )
Part C: Rotate∆A’B’C’ 90 degrees clockwise.
A’’( , ) B’’ ( , ) C’’ ( , )
5) The table below shows the coordinates of triangle RST and the coordinates of R' in triangle R'S'T'. Triangle R'S'T' is a dilation of triangle RST.
Triangle
RST / Triangle
R'S'T'
R / (-2, -3) / R' / (-6, -9)
S / (0,2) / S'
T / (2, -3) / T'
Part A: What are the coordinates of point S' and point T'?
S' = (____, ____) T' = (____, ____)
Part B
On the grid below, draw triangle RST and triangle R'S'T'
6) Trapezoid MNOP is plotted on the grid below.
On the grid, draw the image of trapezoid MNOP after a reflection over the x -axis. Label the coordinates of each point on the new figure.

7) Triangle ABC and triangle A'B'C' are plotted on the coordinate plane below.
What is the name of the transformation applied to triangle ABC that resulted in triangle A'B'C' ?
Answer ______
On the lines below, describe how the coordinates of Point A changed to the coordinates of Point A'.