Grade 8 Transformations Test – Free PDF

Contents

This grade 8 transformations test checks translations, reflections and rotations in 45 minutes, with 8 questions for a total of 20 points.

This test has 8 questions worth 20 points on translations, reflections and rotations (8.G.A.1, 8.G.A.3). All rotations are counterclockwise about the origin. Show your work, plot on the coordinate planes if needed, and plan on 45 minutes.

Test information

Grade: Grade 8
Chapter: Translations, Reflections and Rotations
Common Core: 8.G.A.1, 8.G.A.3
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 3 pts; Question 3: 3 pts; Question 4: 3 pts; Question 5: 3 pts; Question 6: 2 pts; Question 7: 2 pts; Question 8: 2 pts)

Grade 8 Transformations Test: questions 1–5

Question 1: Move a point (2 points)

Point \(P(-3,4)\) is moved.

Translate \(P\) 5 units right and 6 units down. Write the image. (1 point)
Reflect \(P\) across the \(x\)-axis. Write the image. (1 point)

Question 2: Rotate a point (3 points)

Point \(R(2,-5)\) is rotated about the origin counterclockwise. Write the image after a rotation of (a) \(90^{\circ}\), (b) \(180^{\circ}\), (c) \(270^{\circ}\). (1 point each)

Question 3: Translate a triangle (3 points)

Translate triangle \(ABC\) by the rule \((x,y)\to(x+7,\,y-3)\). Write the coordinates of \(A^{\prime}\), \(B^{\prime}\) and \(C^{\prime}\).

Triangle \(ABC\).

Question 4: Reflect a triangle (3 points)

Reflect triangle \(DEF\) across the \(y\)-axis. Write the image vertices. (1 point)
Reflect triangle \(DEF\) across the \(x\)-axis. Write the image vertices. (1 point)
In triangle \(DEF\), side \(DE=4\) units and \(\angle D=45^{\circ}\). Write the length of the image of \(DE\) and the measure of the image of \(\angle D\) for part (a). (1 point)

Triangle \(DEF\).

Question 5: Rotate a triangle (3 points)

Rotate triangle \(GHJ\) by \(90^{\circ}\) counterclockwise about the origin. Write the image vertices.

Triangle \(GHJ\).

Grade 8 Transformations Test: questions 6–8

Question 6: Name the motion (2 points)

Triangle \(ABC\) has vertices \(A(1,3)\), \(B(4,3)\), \(C(1,5)\). Its image has vertices \(A^{\prime}(-1,-3)\), \(B^{\prime}(-4,-3)\), \(C^{\prime}(-1,-5)\). Name the single rigid motion that was used and write its rule.

Question 7: Properties of rigid motions (2 points)

Parallelogram \(ABCD\) has \(AB=7\text{ in}\), \(BC=4\text{ in}\) and \(\angle A=60^{\circ}\). It is rotated \(90^{\circ}\) about the origin to form \(A^{\prime}B^{\prime}C^{\prime}D^{\prime}\). Find \(A^{\prime}B^{\prime}\), \(B^{\prime}C^{\prime}\) and \(\angle A^{\prime}\), and tell whether \(\overline{A^{\prime}B^{\prime}}\) and \(\overline{C^{\prime}D^{\prime}}\) are parallel.