Chapter 18: Review

Resolve the chapter problem

Enlarge each coordinate of the mural tile by $2$ about the origin. The image corners are $(2,2)$, $(6,2)$ and $(2,4)$. The corner $(3,1)$ is farthest from the origin before and after enlargement: its squared distance changes from $3^2+1^2=10$ to $6^2+2^2=40$, so its distance doubles.

For the smaller reversed copy, use scale factor $-\frac12$ on the original corners. The images are $(-0.5,-0.5)$, $(-1.5,-0.5)$ and $(-0.5,-1)$. The negative sign places each point across the origin; the magnitude halves each length.

Mixed practice

For each item, choose a method and explain why it applies.

1. Reflect $(4,-2)$ in the $y$-axis.
2. A shape with length $5$ cm is enlarged to $12$ cm. Find the scale factor.
3. Two triangles have matching three side lengths. State a congruence criterion.
4. Similar shapes have length factor $3$. Find their area factor.
5. A temperature rises from $-4$ to $7$. Work out the change.
6. Solve $4x+3=19$.
7. A point $(2,5)$ is enlarged by factor $-2$ about the origin.
8. Similar solids have volume ratio $1:64$. Find their length ratio.

Reflect

Write one sentence about a method you can now choose confidently. Name one question you would like to practise again.