Question

23 the figure below shows trapezoid mnop on a coordinate plane. if the trapezoid is dilated by a scale factor of 1/2 with the origin as the center of dilation, what are the coordinates of vertex o of the dilated trapezoid mnop? a (15/2, 3) c (6, 6) b (3, 15/2) d (3, 6)

Explanation:

Step1: Identify original coordinates of O

From the graph, the coordinates of vertex O are (6, 6).

Step2: Apply dilation formula

For a dilation with scale - factor \(k=\frac{1}{2}\) and center of dilation at the origin \((0,0)\), the formula for the coordinates of a dilated point \((x,y)\) to \((x',y')\) is \(x' = kx\) and \(y'=ky\). Here, \(x = 6\) and \(y = 6\), \(k=\frac{1}{2}\). So \(x'=\frac{1}{2}\times6 = 3\) and \(y'=\frac{1}{2}\times6 = 3\).

Answer:

A. \((\frac{3}{1},3)\)