Math Core

This test covers translations, reflections, rotations, compositions of transformations, symmetry and dilations.

Question 1

Translate the point $(7, -3)$ by the vector $\langle -9, 5 \rangle$ . What is the image?

Enter a point like (2, -3)

Question 2

A translation maps $A(-1, 4)$ to $A'(3, -2)$ . Which rule describes the translation?

Question 3

Reflect the point $(-6, 2)$ over the line $y = x$ . What is the image?

Enter a point like (2, -3)

Question 4

Reflect the point $(3, -5)$ over the line $x = -2$ . What is the image?

Enter a point like (2, -3)

Question 5

A reflection maps $P(-3, 1)$ to $P'(1, 5)$ . What is the line of reflection?

Triangle ABC and its image A′B′C′.Open in grapher →

Question 6

Which single transformation maps triangle $ABC$ onto triangle $A'B'C'$ in the graph above?

Question 7

Rotate the point $(4, -3)$ $90^\circ$ counterclockwise about the origin. What is the image?

Enter a point like (2, -3)

Question 8

Rotate the point $(6, 2)$ $90^\circ$ counterclockwise about the point $(3, -1)$ . What is the image?

Enter a point like (2, -3)

Question 9

Reflect the point $(2, 5)$ over the x-axis, and then translate the image by $\langle -3, 4 \rangle$ . What is the final image?

Enter a point like (2, -3)

Question 10

A figure is reflected over the line $y = 1$ and then over the line $y = 6$ . The result is a translation. How many units does each point move?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

Which quadrilateral has exactly $4$ lines of symmetry and rotational symmetry of order $4$ ?

Question 12

What is the smallest positive angle, in degrees, of a rotation that maps a regular 20-sided polygon onto itself?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

Dilate the point $(-2, 7)$ by a scale factor of $3$ with center $(1, 1)$ . What is the image?

Enter a point like (2, -3)

Question 14

A figure with area $50$ square units is dilated by a scale factor of $\dfrac{2}{5}$ . What is the area of the image, in square units?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

Which property is preserved by every translation, reflection, rotation and dilation?