Transformations and Congruence: math test, Grade 8 – download the PDF

1 Translation / 4 pts

Triangle \(ABC\) has \(A(-4,\,1)\), \(B(-1,\,1)\), \(C(-4,\,5)\). Translate it by \(\langle 7,\,-3\rangle\).

1. Give \(A'\), \(B'\), \(C'\).
2. Find \(AC\) and \(A'C'\). What do you notice?

2 Reflections / 3 pts

Point \(M\) is \((-6,\,-2)\). Find its image (a) across the x-axis and (b) across the y-axis. (c) How far is \(M\) from the y-axis, and how far is the image in (b)?

3 Rotations / 4 pts

Point \(P\) is \((3,\,4)\). Find its image under a rotation about the origin of (a) \(90^\circ\) counterclockwise, (b) \(180^\circ\), (c) \(90^\circ\) clockwise. (d) Show that all three images are 5 units from the origin.

4 True or false? / 3 pts

Decide whether each statement is true or false, and justify in one sentence.

1. A rotation changes the angle measures of a polygon.
2. Two squares with side 4 cm are congruent.
3. Two rectangles that each have a perimeter of 20 cm are congruent.

5 A sequence of transformations / 4 pts

Triangle \(DEF\) has \(D(1,\,2)\), \(E(4,\,2)\), \(F(1,\,6)\). Reflect it across the x-axis, then translate it by \(\langle -2,\,3\rangle\).

1. Give the final vertices \(D_2\), \(E_2\), \(F_2\).
2. Find the perimeter of \(\triangle D_2E_2F_2\). (\(DE=3\), \(DF=4\), \(EF=5\).)

6 Game sprite / 2 pts

A sprite is at \((2,\,8)\). It is reflected across the y-axis, then moved 5 units down. Give its position after each step.