Invariants Under Transformation Math Example 2

Solution

1. 1
   Apply dilation: multiply each coordinate by $2$. New vertices: $(0,0)$, $(12,0)$, $(12,8)$, $(0,8)$.
2. 2
   Original side lengths: $6$ and $4$. New side lengths: $12$ and $8$. Side lengths are NOT invariant — they doubled.
3. 3
   Original angles: all $90°$. New angles: all $90°$. Angles ARE invariant under dilation.
4. 4
   Original area: $24$. New area: $96 = 24 \times 4 = 24 \times 2^2$. Area scales by $k^2$ so it is NOT invariant.
5. 5
   The ratio of sides: $6:4 = 3:2$ and $12:8 = 3:2$. Ratios of corresponding lengths ARE invariant.