Study Guide and Intervention (continued) - MathnMind

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Study Guide and Intervention (continued)
Transformations on the Coordinate Plane
Transform Figures on the Coordinate Plane You can perform transformations
on a coordinate plane by changing the coordinates of each vertex. The vertices of the image
of the transformed figure are indicated by the symbol , which is read prime.
Reflection over x-axis (x, y) → (x, y)
Reflection over y-axis (x, y) → (x, y)
Translation (x, y) → (x a, y b)
Dilation (x, y) → (kx, ky)
Rotation 90 counterclockwise (x, y) → (y, x)
Rotation 180 (x, y) → (x, y)
Example
A triangle has vertices A(1, 1), B(2, 4), and C(3, 0). Find the
coordinates of the vertices of each image below.
a. reflection over the x-axis
To reflect a point over the x-axis,
multiply the y-coordinate by 1.
A(1, 1) → A(1, 1)
B(2, 4) → B(2, 4)
C(3, 0) → C(3, 0)
The coordinates of the image vertices are
A(1, 1), B(2, 4), and C(3, 0).
Exercises
b. dilation with a scale factor of 2
Find the coordinates of the dilated figure
by multiplying the coordinates by 2.
A(1, 1) → A(2, 2)
B(2, 4) → B(4, 8)
C(3, 0) → C(6, 0)
The coordinates of the image vertices are
A(2, 2), B(4, 8), and C(6, 0).
Find the coordinates of the vertices of each figure after the given transformation
is performed.
1. triangle RST with R(2, 4), S(2, 0), T(1, 1) reflected over the y-axis
2. triangle ABC with A(0, 0), B(2, 4), C(3, 0) rotated about the origin 180°
3. parallelogram ABCD with A(3, 0), B(2, 3), C(3, 3), D(2, 0) translated 3 units down
4. quadrilateral RSTU with R(2, 2), S(2, 4), T(4, 4), U(4, 0) dilated by a factor of
5. triangle ABC with A(4, 0), B(2, 3), C(0, 0) rotated counterclockwise 90°
6. hexagon ABCDEF with A(0, 0), B(2, 3), C(0, 4), D(3, 4), E(4, 2), F(3, 0) translated
2 units up and 1 unit to the left
© Glencoe/McGraw-Hill 220 Glencoe Algebra 1
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