Geo EOC Review: Transformations and Congruency and Similarity

The vertices of 𝛥𝑃𝑄𝑅 are 𝑃(5, 3), 𝑄(– 7, 2), 𝑅(0, – 8). If 𝛥𝑃𝑄𝑅 is transformed following the rule (𝑥, 𝑦) → (𝑥 − 9, 𝑦 + 5), what are the coordinates of the vertices of 𝛥𝑃′𝑄′𝑅′?

• 𝑃(−4, 3), 𝑄(– 16, 2), 𝑅(−9, −8)

• 𝑃(−4, 8), 𝑄(– 16, 7), 𝑅(−9, −3)

• 𝑃(3, −4), 𝑄(2, −16), 𝑅(−8, −9)

• 𝑃(8, −4), 𝑄(7, −16), 𝑅(−3, −9)

Which transformation on the coordinate plane preserves only the angle measure?

• Reflection across the line 𝑦 = −3𝑥.

• Rotation of 270° clockwise about the origin.

• Dilation with scale factor of 1 not centered in the origin.

• Dilation with scale factor of 1.5 centered in the origin.

Triangle 𝐴𝐵𝐶 and triangle 𝐴𝐷𝐸 are shown.

Select all of the transformations that could be performed to carry triangle 𝐴𝐵𝐶 onto triangle 𝐴𝐷𝐸.

• A reflection across the line 𝑦 = −𝑥.

• A reflection across the 𝑥-axis, and then a reflection across the 𝑦-axis.

• A rotation of 90 degrees clockwise about the origin, and then a reflection across the 𝑦-axis.

• A rotation of 90 degrees clockwise about the origin, and then a reflection across the 𝑥-axis.

• A rotation of 180 degrees clockwise about the origin and then a reflection across the line 𝑦 = −𝑥.

The figure below shows two perpendicular lines 𝑗 and 𝑘 intersecting at point 𝐷 in the interior of a rectangle. Line 𝑗 bisects both the top and bottom sides of the rectangle. Line 𝑘 bisects both the left and right sides of the rectangle. Which transformation will always carry the figure onto itself?

Select All that apply.

• a reflection across line 𝑗.

• A reflection across line 𝑘.

• A rotation of 90° clockwise about point 𝐷.

• A rotation of 180° clockwise about point 𝐷.

• A rotation of 270° clockwise about point 𝐷.

If triangle 𝐴𝐵𝐶 with coordinates 𝐴(1, 1), 𝐵(2, 1), 𝐶(2, 2) is reflected across the 𝑥-axis and then dilated by a factor of 3 about the origin, which set of coordinates represents 𝛥𝐴′𝐵′𝐶′?

• 𝐴′(1, −1), 𝐵′(2, −1), 𝐶′(2, −2)

• 𝐴′(−1, 1), 𝐵′(−2, 1), 𝐶′(−2, 2)

• 𝐴′(−3, 3), 𝐵′(−6, 3), 𝐶′(−6, 6)

• 𝐴′(3, −3), 𝐵′(6, −3), 𝐶′(6, −6)

Complete the proof below.

• Statement 3: 𝐴𝐵̅̅̅̅ ≅ 𝐴𝐶̅̅̅̅

  Reason 4: Vertical Angles Theorem

  Reason 5: ASA

• Statement 3: 𝐴𝐵̅̅̅̅ ≅ 𝐹𝐵̅̅̅̅

  Reason 4: Reflexive Property

  Reason 5: AAS

• Statement 3: 𝐴𝐵̅̅̅̅ ≅ 𝐹𝐵̅̅̅̅

  Reason 4: Vertical Angles Theorem

  Reason 5: ASA

• Statement 3: 𝐴𝐵̅̅̅̅ ≅ 𝐴𝐶̅̅̅̅

  Reason 4: Reflexive Property

  Reason 5: AAS

In the figure shown, what is the value of 𝑥 and 𝑦?

• 𝑥 = 5 and 𝑦 = 4

• 𝑥 = 6 and 𝑦 = 7

• 𝑥 = 7 and 𝑦 = 6

• 𝑥 = 4 and 𝑦 = 5

In the figure below quadrilateral 𝐽𝐾𝐿𝑀 is similar to quadrilateral 𝑁𝑃𝑄𝑅. Select All the true statements.

• 𝑥 = 2

• 𝑥 = 6

• 𝑦 = 3

• 𝑚∠𝑃 = 50°

• 𝑚∠𝑅 = 85°

The city aquarium has Koi pond in the shape of a regular pentagon. Shahin wants to build a similar Koi pond in his back yard. What is the perimeter of the new pond. Drawings of both ponds are shown.

• 8.3 𝑓𝑡

• 25 𝑓𝑡

• 26.7 𝑓𝑡

• 80 𝑓𝑡.

Jorge is planning to buy a pool table for his new home. He knows that regulation pool tables are similar. A 9-foot table has a rectangular playing surface that is 100 inches long and 50 inches wide. He is considering an 8-foot table that has a rectangular playing surface that is 88 inches long. Find the area of the playing surface of the 8-feet pool table.