Question

tony performs a dilation on figure r. he uses a scale factor of 4 with a center of dilation at the origin.
what are the coordinates of the image of vertex p?
choose one option from each drop - down menu to answer the question.
the coordinates of the image of vertex p are ( , )

Explanation:

Step1: Recall the dilation formula

For a dilation with center at the origin \((0,0)\) and scale factor \(k\), if a point \(P(x,y)\) is dilated, the image \(P'(x',y')\) has coordinates \((kx,ky)\).

Step2: Identify the coordinates of point \(P\)

From the graph, the coordinates of point \(P\) are \((1,4)\). The scale factor \(k = 4\).

Step3: Calculate the new coordinates

Using the formula \(x'=k\times x\) and \(y'=k\times y\), substitute \(x = 1\), \(y = 4\), and \(k = 4\). So \(x'=4\times1=4\) and \(y'=4\times4 = 16\).

Answer:

\((4,16)\)