Final Exam Review

△J′K′L′ is the image produced by reflecting △JKL across the y-axis. The

coordinates of J′ are (1, 7). What are the coordinates of J?

• (-7, 1)

• (7, -1)

• (-1, 7)

• ( 1, -7)

A triangle has vertices at R(-6, -1), S(-3, -1), and T(-5, -4). It goes through a series of transformations to create an image with vertices at R’(-9, 0), S’(0, 0), and T’(-6, -9). Which series of transformations could create △R’S’T’?

• a translation of right 3 units and 1 unit up, followed by a dilation of scale factor 3 about the origin

• a translation of right 1 unit and 3 units up, followed by a dilation of scale factor 3 about the origin

Triangle MPT is shown on this graph. Which set of transformations will not construct a triangle congruent to MPT?

• a reflection over the x-axis, then a translation of right 3 units and down 2 units

• a dilation of 1/4 centered at the origin, then a rotation of 180° about the origin, then a dilation of 2 centered at the origin

• a dilation of 3 centered at the origin, then a reflection over the x-axis, then a dilation of 1/3 centered at the origin

• a translation of down 3 units, then a reflection over the x-axis

The triangle shown will be rotated 180° about the origin. Which transformation will result in the triangle moving back to its original location?

• a reflection over the line y = -x

• a 90° clockwise rotation about the origin, followed by a reflection over the x-axis

• a reflection over the x-axis, followed by a reflection over the y-axis

• a reflection over the line y = x, followed by a 90° counterclockwise

  rotation about the origin

In the graph below, △P′Q′R′ is the image produced by applying a translation to △PQR. Which rule describes the translation?

• (x′, y′) = (x – 3, y + 5)

• (x′, y′) = (x + 3, y – 5)

• (x′, y′) = (x – 3, y – 5)

• (x′, y′) = (x + 3, y + 5)

A polygon will be rotated 90 degrees counterclockwise about the origin and then dilated with respect to the origin by a scale factor of 2. Which choice describes the overall transformation, f?

• f(x, y) = (-2x, 2y)

• f(x, y) = (-2x, -2y)

• f(x, y) = (-2y, -2x)

• f(x, y) = (-2y, 2x)

A line segment has endpoints P(2, 3) and Q(4, 6). It is dilated by a scale factor of 3 with a center of dilation at (0, 6). Which statement is true?

• The preimage and image are parallel, and the image 1/3 length of the preimage.

• The preimage and image intersect, and the image 1/3 length of the preimage.

• The preimage and image are parallel, and the image is 3 times the length of the preimage.

• The preimage and image intersect, and the image is 3 times the length of the preimage.

Angle 1 is congruent to angle 2 in this diagram. Which statement about the diagram must be true, and why?

• Line j is parallel to line k. If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

• Line l is parallel to line m. If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

• Line j is perpendicular to line l. If two lines form to make right angles, then the lines are perpendicular.

• Line k is perpendicular to line l. If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are perpendicular.

• The value of x₂ must be decreased by 4 units.

• The value of y₁ must be increased by 4 units.

• The value of y₂ must be decreased by 4 units.

• The value of x₂ must be increased by 4 units.