Question

find the image based on the graph of the pre - image. dilation of $\frac{1}{4}$ about the origin 26. find w

Explanation:

1. First, assume the coordinates of point \(W\):

• From the graph, assume the coordinates of point \(W\) are \((x,y)\). Let's say by observing the grid, \(W\) is at \((- 2,4)\).

1. Then, use the dilation - rule for a dilation about the origin:

• The rule for a dilation of scale factor \(k\) about the origin is \((x,y)\to(kx,ky)\). Here, \(k = \frac{1}{4}\).
• For point \(W(-2,4)\), when we apply the dilation, we calculate the new \(x\) - coordinate as \(x'=k\times x=\frac{1}{4}\times(-2)=-\frac{1}{2}\), and the new \(y\) - coordinate as \(y'=k\times y=\frac{1}{4}\times4 = 1\).

Answer:

The coordinates of \(W'\) are \((-\frac{1}{2},1)\)