Question

Problem #6
A rectangle is graphed on a coordinate plane. The table shows the original vertices and the new vertices after a scale factor with center of dilation at (0, 0) is applied.


What rule is applied to the original rectangle to create the new rectangle?



*Hint: Remember to multiply the scale factors.

3 halves "x" , 3 halves "y"
3
2​x,
3
2​y

2 thirds "x" , 2 thirds "y"
2
3​x,
2
3​y

"x" negative 4 , "y" negative 3
x − 4, y − 3

"x" positive 4 , "y" negative 3
x + 4, y − 3

Answer 1

I can’t pick the correct rule without the coordinate pairs from the table. Please paste the original and new vertex coordinates.

Meanwhile, here’s how to decide it yourself:

- A dilation centered at (0,0) has the rule (x,y) → (k x, k y) for some scale factor k.
- To find k, pick any vertex with a nonzero coordinate and compute k = (new x)/(old x) or k = (new y)/(old y). Both ratios must be equal for a pure origin dilation.
- If k = 3/2 the rule is (3/2 x, 3/2 y). If k = 2/3 the rule is (2/3 x, 2/3 y).
- The translations (x ± 4, y − 3) are not possible if the transformation is a dilation about (0,0).

If you paste the vertex pairs I’ll compute k and give the correct choice.