Translations, Reflections and Rotations: Grade 8 Math Test – PDF Download

Question 1: Move a point (2 points)

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

1. Translate \(P\) 5 units right and 6 units down. Write the image. (1 point)
2. 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 \(C^{\prime}\).

Question 4: Reflect a triangle (3 points)

1. Reflect triangle \(DEF\) across the \(y\)-axis. Write the image vertices. (1 point)
2. Reflect triangle \(DEF\) across the \(x\)-axis. Write the image vertices. (1 point)
3. 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)

Question 5: Rotate a triangle (3 points)

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

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.

Question 8: Find the original point (2 points)

Point \(S^{\prime}\) is at \((4,-7)\) after a \(270^{\circ}\) counterclockwise rotation about the origin. Find the original point \(S\).

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