Rigid Transformations: Geometry Math Test – PDF Download

Question 1: Translate a triangle (2 points)

Translate triangle \(ABC\) by \(\langle -4,\,3\rangle\). Write the coordinates of the three image vertices.

Question 2: Reflect over y = x (2 points)

Reflect triangle \(JKL\) over the line \(y=x\). Write the coordinates of the image vertices.

Question 3: Rotate clockwise (2 points)

Rotate each point \(90^{\circ}\) clockwise about the origin.

1. \((3,\,2)\)
2. \((-4,\,5)\)
3. \((0,\,-6)\)

Question 4: Sequence of transformations (3 points)

Triangle \(DEF\) has vertices \(D(1,\,2)\), \(E(4,\,2)\), \(F(1,\,6)\). It is reflected over the y-axis and then translated by \(\langle 2,\,-3\rangle\).

1. Find the coordinates of the final image. (2 points)
2. Show that side \(DE\) has the same length as its final image. (1 point)

Question 5: Identify the transformation (2 points)

Triangle \(ABC\) is mapped onto triangle \(A^{\prime}B^{\prime}C^{\prime}\). Name the transformation and describe it completely.

Question 6: Rigid or not rigid (2 points)

The rule \((x,\,y)\) to \((x,\,3y)\) is applied to segment \(AB\) with \(A(1,\,1)\) and \(B(1,\,4)\).

1. Find the length of \(AB\) and the length of its image. (1 point)
2. Is the rule a rigid transformation? Explain. (1 point)

Question 7: Symmetry (3 points)

A regular octagon is shown.

1. How many lines of symmetry does it have? (1 point)
2. What is the smallest positive rotation about its center that maps it onto itself? (1 point)
3. How many lines of symmetry does a rectangle that is not a square have? (1 point)

Question 8: Describe a sequence (2 points)

Rectangle \(ABCD\) is mapped onto rectangle \(A^{\prime}B^{\prime}C^{\prime}D^{\prime}\) by a sequence of two rigid transformations. Describe one such sequence.

Question 9: Robot position (2 points)

Diego programs a robot that starts at \((-3,\,4)\) on a grid. It reflects over the x-axis and then moves by the vector \(\langle 5,\,2\rangle\). Where does it end?

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