Question

Find the coordinates of each point under the given dilation 2. (6,3); scale factor of 1/3, center of dilation at the at the origin.

Answer 1

The coordinate of the new point after dilation is (2, 1)

Step-by-step explanation:
`\begin{gathered} 2)\text{ The given point = (6, 3)} \\ \text{The scale factor = 1/3The center of dilation is at origin (0, 0)} \end{gathered}`

For dilation, the scale factor is applied to both the x and y coordinate:

`\begin{gathered} (x,\text{ y) }\rightarrow\text{ (kx, ky)} \\ \text{where k = scale factor} \end{gathered}`
`\begin{gathered} \text{ Since the center of dilation is at point (0, 0),} \\ we\text{ will mutiply the x and y coordinates in the given point by 1/3} \\ \\ (6,\text{ 3) }\rightarrow\text{ (}(1)/(3)*6,\text{ }(1)/(3)*3) \\ =\text{ (2, 1)} \end{gathered}`

The coordinate of the new point after dilation is (2, 1)