Question

the figure below is dilated with the center of dilation at the origin and a scale factor of 1/3. what are the coordinates of the image of point r after this transformation?

Explanation:

1. First, identify the coordinates of point \(R\):

• By observing the graph, the coordinates of point \(R\) are \((3,-6)\).

1. Then, use the dilation - rule for a dilation centered at the origin with scale factor \(k\):

• The rule for dilation centered at the origin \((0,0)\) with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here, \(k = \frac{1}{3}\), \(x = 3\), and \(y=-6\).
• Calculate the \(x\) - coordinate of the dilated point:
• \(x_{new}=k\times x=\frac{1}{3}\times3 = 1\).
• Calculate the \(y\) - coordinate of the dilated point:
• \(y_{new}=k\times y=\frac{1}{3}\times(-6)=-2\).

Answer:

The coordinates of the image of point \(R\) are \((1, - 2)\).