Question

kaylee designs a logo for her art club, represented by figure stuvw. she enlarges the logo to form image stuvw. kaylee uses a scale factor of 3 with a center of dilation at the origin. what are the coordinates of u? use the number pad to enter your answers in the boxes. u( , )

Explanation:

Step1: Determine original coordinates of U

From the graph, the coordinates of point U are (4, 5).

Step2: Apply dilation formula

For a dilation with scale - factor \(k = 3\) and center of dilation at the origin \((0,0)\), the formula to find the coordinates of the dilated point \((x',y')\) from the original point \((x,y)\) is \(x'=k\times x\) and \(y'=k\times y\). Here, \(x = 4\) and \(y = 5\), \(k = 3\). So \(x'=3\times4 = 12\) and \(y'=3\times5 = 15\).

Answer:

\(U'(12,15)\)