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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.

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.

Is Δ ABC Δ EDF an isometry?

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

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

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

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 .

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.

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).

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

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

Prove that a translation is an isometry.

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

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 .

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

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

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.)

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)

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

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

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.

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 .

How would you construct line j so that ?

( R _{ a } denotes a reflection about line a .)

Complete:

If , then .

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