Transformations Questions

Translation

Question 1

Draw the image after translating the triangle $EDF$ 2 units to the left and 1 unit upwards.

Question 2

Describe the following translation where triangle $ABC$ is mapped onto triangle $A'B'C'$.

Question 3

The point $A(-2,5)$ is translated 1 unit to the right and 5 units downwards. Find the coordinates of the image $A'$.

Question 4

The point $B(0,1)$ is translated and the resulting image is $B'(1,-2)$. Describe the translation.

Answers (translation)

Question 1

Question 2

2 units to the left and 1 unit upwards.

Question 3

$A'(-1,0)$.

Question 4

1 unit to the right and 3 units downwards.

Dilation

Question 1

For questions a and b, perform the dilation with the stated scale factors centered about the origin $O$ marked on the diagram.

Question 2

Find the scale factor in the following dilations.

Question 3

Find the center of the dilation and the scale factor where the triangle $ABC$ is mapped onto triangle $A'B'C'$.

Question 4

The point $A(-10,-2)$ is dilated by a factor of 3 using point $P(-8,2)$ as the center. Find the coordinates of the image $A'$.

Answers (dilation)

Question 1

Question 2

(a) $2$.

(e) $\frac{1}{3}$.

Question 3

$(0,0), 2$.

Question 4

$A'(-14,-10)$.

Reflection

Question 1

Question 2

Question 3

(a) The point $A(2,5)$ is reflected about the $x$-axis. Find the coordinates of the image $A'$.

(b) The point $B(6,3)$ is reflected about the line $x=4$. Find the coordinates of the image $B'$.

Question 4

The point $A(6,-5)$ is mapped to its image $A' (-6,-3)$ by two successive reflections. What are the lines of reflection?

Answers (reflection)

Question 1

Question 2

Question 3

(a) $A'(2,-5)$.

(b) $B'(2,3)$.

Question 4

The line $y=-4$ and the $y$-axis.

Rotation

Question 1

Rotate the triangle $90^\circ$ anti-clockwise about $O$.

Question 2

Question 3

Question 4

Question 5

Triangle $ABC$ has vertices $A(4,1)$, $B(3,4)$ and $C(1,2)$. Find the coordinates of the image of $\triangle ABC$ after a roation of $90^\circ$ counter-clockwise about the origin.

Answers (rotation)

Question 1

Question 2

(a) $180^\circ$ anti-clockwise (can be clockwise as well) about $O$.

(b) $90^\circ$ clockwise about $O$.

(d) $90^\circ$ anti-clockwise about $O$.

Question 3

$90^\circ$ clockwise about $O$.

Question 4

(a) 4.

(b) 2.

(d) 8.

(e) 3.

(f) 1.

Question 5

$A'(-4,-1)$, $B'(-4,-3)$, $C'(-2,-1)$.