Math Homework. Do It Faster, Learn It Better.
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Chapter: Transformations Section: Exercises

Problem: 1

X (3, 5), Y (4, 1), and Z (2, 2) are the vertices of triangle XYZ . Draw the triangle and its reflection image in the line y = 3.


Problem: 2

Quadrilateral PQRS has the vertices P (2, 5), Q (4, 4), R (3, 1), and S (1, 2). After a translation of the figure, the image of point R is the origin. Graph quadrilateral PQRS and its image.


Problem: 3

Is Δ ABC Δ EDF an isometry?


Problem: 4

Determine the coordinates of the figure shown after it is translated 5 units up, then reflected across the y –axis.


Problem: 5

Copy the given figure on graph paper. Then sketch the image by reflection in line l .


Problem: 6

If P (0, 9), Q (–6, 0), and R (–6, –9), graph Δ PQR and its reflection over the line y = x .


Problem: 7

Use the given figure. Give the coordinates of the image of the point A by reflection in (a) the x –axis, (b) the y –axis, and (c) the line y = x .


Problem: 8

Graph quadrilateral ABCD for A (3, –2), B (–1, 0), C (–1, 2), D (2, 5). Then reflect the triangle over the line y = 2, and again reflect it over the line y = –2.


Problem: 9

Graph trapezoid ABCD for A (3, 4), B (7, 3), C (7, 0), D (–1, 2). Then translate the trapezoid so that A goes to A' (–7, 2).


Problem: 10

Find T :(4, 4) (?, ?) if T :(0, 0) (3, 2).


Problem: 11

Find T :(?, ?) (0, 0), if T :(–1, 4) (4, 5).


Problem: 12

Prove that a translation is an isometry.


Problem: 13

Rotate the figure 270 about O . Label the image's vertices.


Problem: 14

The lines shown in the figure intersect at O to form 30 angles. The hexagon, quadrilateral, and triangle are regular. Find the image of a 240 rotation of about O .


Problem: 15

The diagonals of a regular hexagon RSTUVW form six equilateral triangles. If denotes a rotation of θ degrees around point X , complete the following:


Problem: 16

If denotes a rotation of θ degrees around point X , give another name for the rotation .


Problem: 17

The notation represents a dilation centered at point X with scale factor k . Use the given figure and obtain the coordinates of the images of A , B , and C by the dilation

(Here O denotes the origin.)


Problem: 18

Obtain the scale factor of the dilation, if a dilation with the origin, O , as center maps the given point to the image point named. Identify whether the dilation is an expansion or a contraction.

(3, 0) (6, 0)


Problem: 19

If segment AB has length 6 and undergoes a dilation with scale factor 2.5, find the length of its image.


Problem: 20

Draw Δ P ' Q ' R ' under the dilation with center A and scale factor 1/4.


Problem: 21

H X denotes a 180 rotation about point X , and denotes a dilation centered at point X and with scale factor k . Make a copy of the given figure twice and show the image of the red stick under the composites given.


Problem: 22

Draw a grid and obtain the coordinates of the image point. O is the origin and A is the point (5, 2). R x and R y are reflections in the x – and y –axes, and D X , k is a dilation centered at point X with scale factor k .


Problem: 23

How would you construct line j so that ?

( R a denotes a reflection about line a .)


Problem: 24


If , then .


Problem: 25

A rule is given for a mapping S . Give the rule for S –1 .