Question

What would be the new coordinates of the following image after a dilation of 3?

Answer 1

Remember that the rule for a dilation by a factor of k about the origin is:

`(x,y)\rightarrow(kx,ky)`

Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.

`\begin{gathered} W=(4,2) \\ X=(8,6) \\ Z=(8,2) \end{gathered}`

Apply a dilation by a factor of 3:

`\begin{gathered} W(4,2)\rightarrow W^(\prime)(3*4,3*2)=W^(\prime)(12,6) \\ X(8,6)\rightarrow X^(\prime)(3*8,3*6)=X^(\prime)(24,18) \\ Z(8,2)\rightarrow Z^(\prime)(3*8,3*2)=Z^(\prime)(24,6) \end{gathered}`

Therefore, the new coordinates would be:

`\begin{gathered} W^(\prime)=(12,6) \\ X^(\prime)=(24,18) \\ Z^(\prime)=(24,6) \end{gathered}`