Space-Camp Mission Simulator: Similarity Checks

Use transformations to compare mission graphics and describe their sequences.

Mission Screen Checks

Each diagram shows the vertices of two triangular graphics. Match vertices in the stated order. All dilations are centered at the origin unless stated otherwise.

The simulator changes triangle ABC into triangle PQR, with A → P, B → Q, and C → R. Which sequence maps all three vertices correctly?

A. Reflect across the x-axis, then dilate by a factor of 2.B. Reflect across the y-axis, then dilate by a factor of 1/2.C. Reflect across the y-axis, then dilate by a factor of 2.D. Rotate 180° about the origin, then dilate by a factor of 2.

A navigation marker changes from triangle ABC to triangle PQR, with A → P, B → Q, and C → R. First rotate 90° counterclockwise about the origin. Then dilate to reach the target.

What is the dilation factor?

A landing-zone graphic changes from triangle ABC to triangle PQR, with A → P, B → Q, and C → R. Which sequence works?

A. Dilate by 1/2, then translate 3 units right and 2 units down.B. Dilate by 2, then translate 3 units right and 2 units down.C. Dilate by 1/2, then translate 2 units right and 3 units down.D. Translate 3 units right and 2 units down, then dilate by 1/2.

A docking symbol changes from triangle ABC to triangle PQR, with A → P, B → Q, and C → R. Which description is correct?

A. No dilation enlarges them, so they cannot be similar figures.B. Their positions differ, so they are neither similar nor congruent.C. A translation maps them, so they are congruent but not similar.D. A translation maps them, so they are both congruent and similar.

Plan the Transformation

Use corresponding vertices and side lengths to check each mission plan. Apply transformations in the order given.

A triangular route overlay has the corresponding vertices shown. Which sequence maps the original overlay to the target?

Route Overlay Coordinates
Vertex	Original (x, y)	Target (x, y)
A → P	(1, 2)	(−2, −4)
B → Q	(4, 2)	(−8, −4)
C → R	(1, 3)	(−2, −6)

A. Reflect across the x-axis, then dilate by 2.B. Reflect across the y-axis, then dilate by 2.C. Rotate 180° about the origin, then dilate by 2.D. Rotate 90° clockwise about the origin, then dilate by 2.

A triangular spacecraft outline has vertices (2, 2), (6, 2), and (2, 4). Dilate by 1/2 about the origin, then translate 4 units left and 3 units up. The image of vertex (2, 4) is (x, y).

x = ; y =

A rectangular sensor panel is 3 units wide and 5 units tall. Its target graphic is 6 units wide and 10 units tall, with the same orientation. The panels may be in different positions. Which plan guarantees a match?

A. Rotate the original panel 90°, then translate it.B. Translate the original panel without changing its size.C. Dilate the original panel by 1/2, then translate it.D. Dilate the original panel by 2, then translate it.

A rectangular warning frame is 4 units by 7 units. The target is a rectangle 8 units by 12 units. Can a sequence of rotations, reflections, translations, and dilations map the original onto the target?

A. No; the side lengths do not share a single dilation factor.B. Yes; doubling the shorter side is enough to establish similarity.C. Yes; every pair of rectangles can be linked by such a sequence.D. No; similar rectangles must have equal corresponding side lengths.

A mission emblem is dilated by 3/2, reflected across the y-axis, and translated 5 units down. A side of the final emblem is 12 units long.

How long was the corresponding original side? units

Mission Review

Check whole figures, not just one vertex or one side. Give a reason when asked.

10.

The simulator must preserve the shape of a navigation graphic. Select every sequence that guarantees an image similar to the original.

11.

A simulator first translates a graphic 3 units right, then dilates it by 2 about the origin. Which sequence always returns the final graphic to the original?

A. Translate 3 units left, then dilate by 1/2 about the origin.B. Dilate by 1/2 about the origin, then translate 3 units left.C. Dilate by 2 about the origin, then translate 3 units left.D. Translate 3 units right, then dilate by 1/2 about the origin.

12.

A triangular signal marker is reflected across the y-axis and dilated by 3. Its original angles are 38°, 67°, and 75°. What are the corresponding image angles, in the same order?

A. The image angles are 75°, 67°, and 38°.B. The image angles are 38°, 67°, and 75°.C. The image angles are 114°, 201°, and 225°.D. The image angles are 41°, 70°, and 78°.

13.

Imani proposes this sequence for a triangular radar graphic: dilate by 2 about the origin, then translate 1 unit right and 1 unit up. She checks only A → P and says the sequence maps the entire triangle. Use the table to evaluate her claim. Explain your reasoning.

Radar Graphic Check
Correspondence	Original (x, y)	Target (x, y)
A → P	(1, 1)	(3, 3)
B → Q	(3, 1)	(7, 3)
C → R	(1, 3)	(3, 8)