9-5 transformations in the coordinate plane learn to use translations, reflections, and rotations to...
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9-5 Transformations in the Coordinate Plane
Learn to use translations, reflections, and rotations to change the positions of figures in the coordinate plane.
9-5 Transformations in the Coordinate Plane
Additional Example 1: Translating Figures in the Coordinate Plane
Translate rectangle ABCD 4 units left. Give the coordinates of each vertex in the image.
Each vertex is translated 4 units right.
x
y
2
2
–2
–4
4
4
–4
–2 The vertices of the image are A’(–3, 2), B’(–1, 2), C’(–3, 1), and D'(–1, 1).
A B
C D
A’ B’
C’ D’
9-5 Transformations in the Coordinate Plane
A' is read “A prime.” Prime notation is used to represent the point on the image that corresponds to the same point on the original figure.
Reading Math
9-5 Transformations in the Coordinate Plane
Check It Out: Example 1
Translate square ABCD 5 units right. Give the coordinates of each vertex in the image.
Each vertex is translated 5 units right.
x
y
2
2
–2
–4
4
4–2
DC
BAThe vertices of the image are A’(–4, 1), B’(–1, 1), C’(–4, –4), and D'(–1, –4).
A' B'
C' D'
9-5 Transformations in the Coordinate Plane
Additional Example 2: Reflecting Figures in the Coordinate Plane
x
y
T
R
4
4
–4
Reflect triangle RST across the y-axis. Give the coordinates of each vertex in the image.
Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure.
The vertices of the image are R’(–1, 0), S’(–2, 2), and T’(–2, –2).
S
T’
R’
S’
9-5 Transformations in the Coordinate Plane
A line of reflection is not limited to the x-axis or y-axis. Any line can be a line of reflection.
Helpful Hint
9-5 Transformations in the Coordinate Plane
Check It Out: Example 2
x
y
A
B
C
3
–3
Reflect triangle ABC across the x-axis. Give the coordinates of each vertex in the image.
Each vertex of the image is the same distance from the y-axis as the corresponding vertex in the original figure.
The vertices of the image are A’(1, 0), B’(3, –3), and C’(5, 0).
A’
B’
C’
9-5 Transformations in the Coordinate Plane
Rotate triangle JKL 90° counter-clockwise about the origin. Give the coordinates of each vertex in the image.
Additional Example 3: Rotating Figures in the Coordinate Plane
Notice that the vertex K is 3 units to the right of the origin, and vertex K is 3 units above the origin.Similarly, vertex L is 1 unit to the right of the origin, and vertex L' is 1 unit above the origin.
x
y
2
–2
K'
J'
L'
J
KL–2 2
The vertices of the image are J’(–2, 2), K’(0, 3), and L’(0, 1).
9-5 Transformations in the Coordinate Plane
Rotate triangle JKL 180° counter-clockwise about the origin. Give the coordinates of each vertex in the image.
Check It Out: Example 3
The vertices of the triangle are ADC are A’(–3, –1), D’(0, 0), and C’(2, –2).
Notice that the vertex D’ remains on the origin.