9.4 Transformations, Congruence and Similarity

Reflect the point $(-2, 5)$ in the $x$-axis.

Reflect the point $(-2, 5)$ in the $y$-axis.

Translate $(2, -1)$ by the vector $(4, 3)$. State the image.

Rotate $(3, 0)$ by 90° anticlockwise about the origin. State the image.

Triangle ABC has $A(1,1), B(2,1), C(1,3)$. Enlarge by sf 2 from the origin. State $A', B', C'$.

Two figures are similar with scale factor 3. The smaller has length 5 cm. Find the corresponding length on the larger.

Two triangles A and B are similar. A: sides 3, 4, 5. B: shortest side 6. Find B's other sides.

Two triangles are congruent. State the four uniqueness rules.

Reflect the point $(3, 4)$ in the line $y = x$. State the image.

Two similar shapes have linear scale factor 2. The smaller has area 16 cm². Find the larger area.

Two similar rectangles have areas 18 cm² and 162 cm². The smaller's shorter side is 3 cm. Find the larger's shorter side.

A triangle has vertices $A(0,0), B(2,0), C(0,2)$. Reflect in the $y$-axis to find $A', B', C'$.

Translate $\triangle ABC$ with $A(1, 2), B(3, 2), C(2, 4)$ by vector $(2, -1)$. State the image vertices.

A square with vertices $A(1,1), B(3,1), C(3,3), D(1,3)$ is enlarged by factor 2 about the origin. State the image vertices.

Rotate $\triangle ABC$ with $A(1,1), B(2,1), C(1,3)$ by 90° anticlockwise about the origin.

Two similar triangles have a side ratio of $\dfrac{x+2}{15} = \dfrac{x}{12}$. Find $x$.

Two similar prisms have linear scale factor 3. The smaller has volume 27 cm³. Find the larger volume.

A triangle with vertices $(0,0), (4,0), (4,3)$ is reflected in the $x$-axis. State the image area and verify it equals the original.

Two triangles are congruent. State which rule(s) apply when given (a) 3 sides match, (b) 2 sides and the included angle match.

A square with area 25 cm² is enlarged by scale factor 2. Find the new area and verify the rule.

A triangle ABC: $A(1,1), B(3,1), C(2,3)$. Enlarge by sf 2 from origin. State image vertices.

Two triangles share sides $a_1, b_1, c_1$ and $a_2, b_2, c_2$ with corresponding sides equal: $a_1 = a_2, b_1 = b_2$, included angle equal. State the congruence rule.

Triangle ABC is similar to DEF with sf $k = 5/3$ from ABC to DEF. AB = 6, AC = 9. Find DE and DF.

Two similar shapes have areas 18 cm² and 50 cm². Find the linear scale factor.

A triangle has sides 6 cm, 8 cm, 10 cm. A similar triangle has perimeter 36 cm. Find its sides.

Triangle ABC has $A(0, 0), B(4, 0), C(0, 3)$. Rotate 90° clockwise about origin. State the image vertices.

Two similar prisms have surface areas $24$ cm² and $96$ cm². Find the volume ratio.

A rectangle 4 × 6 is enlarged by sf 1.5. Find (a) new dimensions, (b) new area, (c) new perimeter.

A triangle has vertices $A(1, 2), B(4, 2), C(4, 6)$. Reflect in $y = x$ to get image $A', B', C'$.

A triangle PQR has $PQ = 6, QR = 8, RP = 10$. Show ΔPQR is right-angled. Identify the right angle.

A cylindrical glass of radius 6 cm and height 12 cm is full of water. Water is poured into a similar cylindrical glass (radius half of the first). To what height does the water rise?

Triangle ABC is similar to triangle PQR with sf 2 from ABC to PQR. Triangle ABC has area 18 cm². Find PQR's area and perimeter ratio.

A photo is enlarged so its area is doubled. Find the exact linear scale factor.

A triangle is rotated 90° about the origin, then reflected in the $x$-axis. The original is $A(1, 2)$. Find the final image.

Two similar cones have heights 6 and 9. The smaller has slant 8. Find the larger's slant.

Triangle ABC has angles 60°, 80°, 40°. Triangle DEF has angles 60°, 80°, 40°. Are they similar? Are they congruent?

A triangle has area 24 cm². It is enlarged by sf 2.5 from a point. Find the area of the image.

Triangle ABC has $A(0,0), B(3,0), C(0,4)$. It is enlarged by sf 2 from the centre $(1, 1)$. Find the image vertices.

Two similar triangles have linear scale factor 4:7. Their corresponding areas are in what ratio?

A figure of area $A$ is transformed by rotation. Show that the area is preserved.