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Space-Camp Mission Simulator: Similarity Checks

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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.

1.
The simulator changes triangle ABC into triangle PQR, with A → P, B → Q, and C → R. Which sequence maps all three vertices correctly?−6−5−4−3−2−11234560−6−5−4−3−2−1123456ABCPQR
Question 1 options
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.−8−6−4−224680−8−7−6−5−4−3−2−112345678ABCPQR

What is the dilation factor?

3.
A landing-zone graphic changes from triangle ABC to triangle PQR, with A → P, B → Q, and C → R. Which sequence works?−6−5−4−3−2−11234560−6−5−4−3−2−1123456ABCPQR
Question 3 options
4.
A docking symbol changes from triangle ABC to triangle PQR, with A → P, B → Q, and C → R. Which description is correct?−6−5−4−3−2−11234560−6−5−4−3−2−1123456ABCPQR
Question 4 options

Plan the Transformation

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

5.
A triangular route overlay has the corresponding vertices shown. Which sequence maps the original overlay to the target?
Route Overlay Coordinates
VertexOriginal (x, y)Target (x, y)
A → P(1, 2)(−2, −4)
B → Q(4, 2)(−8, −4)
C → R(1, 3)(−2, −6)
Question 5 options
6.
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 =

7.
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?
Question 7 options
8.
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?
Question 8 options
9.
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?
Question 11 options
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?
Question 12 options
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
CorrespondenceOriginal (x, y)Target (x, y)
A → P(1, 1)(3, 3)
B → Q(3, 1)(7, 3)
C → R(1, 3)(3, 8)