Unit 1 Mock Test

A triangle has points A(-2, -3), B(0, 4), and C(2, 4). It is translated 3 units left and 2 units up to form triangle A'B'C'. Triangle A'B'C' is then reflected over the line y = -x for form triangle A''B''C''. What are the vertices of the final triangle A''B''C''?

• A''(-1, 5), B''(-3, -2), and C''(-5, -2)

• A''(5, -1), B''(-2, -3), and C''(-2, -5)

• A''(5, 1), B''(3, -6), and C''(1, -6)

• A''(1, 5), B''(-6, 3), and C''(-6, 1)

This shape has how many lines of symmetry and what angle of rotation?

• 2 lines of symmetry and 180^o angle of rotation

• 0 lines of symmetry and 180^o angle of rotation

• 4 lines of symmetry and 90^o angle of rotation

• 0 lines of symmetry and 90^o angle of rotation

Given rectangle A(7, 2), B(1, 2), C(1, 6), and D(7, 6) is translated by the rule (x, y) → (x - 4, y - 3). What is the perimeter of rectangle A'B'C'D'?

• 10

• 14

• 20

• 48

A square is show in the coordinate grid. Which of the following will preserve the square's angles and side lengths?

• dilation by a scale factor of 4

• horizontal stretch

• translation 12 units down

• vertical stretch

A figure on a coordinate plane is transformed so that its image is congruent to the original figure. Select all of the possible transformations (2).

• f(x, y) → (x + 5, y - 2)

• f(x, y) → (2x, -y)

• f(x, y) → (-x, 1/3y)

• f(x, y) → (y, x)

• f(x, y) → (1/5x, y + 7)

A figure is rotated 180 degrees clock-wise and then reflected over the x-axis, which transformation can be used to map each point (x, y) on the figure to its corresponding point on the image?

• f(x, y) → (-x, y)

• f(x, y) → (x, -y)

• f(x, y) → (-x, -y)

• f(x, y) → (-y, x)

Two transformations of quadrilateral PQRS are described below.

First transformation: f(x, y) → (-x, y)

Second transformation: f(-x, y) → (-x, y + 3)

Which transformation were used on the quadrilateral?

• translation, then a reflection over x-axis

• reflection over x-axis, then a translation

• reflection over y-axis, then a translation

• translation, then a reflection over y-axis

Translation T maps point (3, 5) to (6, 10). Which of the following rules describes the translation T?

• T: (x, y) → (-2x, 2y)

• T: (x, y) → (1/2x, 1/2y)

• T: (x, y) → (x + 3, y + 5)

• T: (x, y) → (x - 3, y - 5)

Identify the transformation from ABC to A'B'C'.

• Reflection across the x-axis

• Reflection across the y-axis

• 90^o clockwise rotation

• 90^o counterclockwise rotation

A triangle is located in the fourth quadrant of a coordinate plane. The triangle is rotated 90° CW and then dilated by a factor of ¼. The image is then rotated 180° CCW and dilated by a factor of 4. Which is a correct answer and explanation to the question: Is the final image congruent to the original triangle?

• Yes, because the rotations cancel the dilations.

• Yes, because the second dilation undoes the first dilation.

• No, because the image has been dilated.

• No, because the image has been moved to a different quadrant.