Question

what are the coordinates of the image of l for a dilation with center (0, 0) and scale factor 0.25?
options:
(4, 16)
(4, 1)
(0.25, 0)
(0.25, 1)

Explanation:

Step1: Recall dilation formula

For a dilation with center \((0,0)\) and scale factor \(k\), the image of a point \((x,y)\) is \((kx, ky)\).

Step2: Identify coordinates of \(L\)

The coordinates of \(L\) are \((1, 4)\).

Step3: Apply dilation formula

Using the scale factor \(k = 0.25\), we calculate the new \(x\)-coordinate as \(1\times0.25 = 0.25\) and the new \(y\)-coordinate as \(4\times0.25 = 1\).

Answer:

\((0.25, 1)\)