Question

What are the coordinates of the image of SABC after a dilation with center (0, 0) and a scale factor of 1/2? Drag numbers to complete thecoordinates. Numbers may be used once, more than once, or not at all

Answer 1

The general rule for a dilation with center in the origin (0,0) is:

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

k is the scale factor.

Then, for the given figure:

Coordinates of original figure:

A(2,2)

B(4,6)

C(6,2)

Coordinates of the dilated imge: k=1/2

$\begin{gathered} A(2,2)\rightarrow A^{\prime}(\frac{1}{2}\cdot2,\frac{1}{2}\cdot2) \\ \\ A(2,2)\rightarrow A^{\prime}(1,1) \end{gathered}$$\begin{gathered} B(4,6)\rightarrow B^{\prime}(\frac{1}{2}\cdot4,\frac{1}{2}\cdot6) \\ \\ B(4,6)\rightarrow B^{\prime}(2,3) \end{gathered}$$\begin{gathered} C(6,2)\rightarrow C^{\prime}(\frac{1}{2}\cdot6,\frac{1}{2}\cdot2) \\ \\ C(6,2)\rightarrow C^{\prime}(3,1) \end{gathered}$

A'(1,1), B'(2,3), C'(3,1)