Question

25 trapezoid mnop is dilated to create trapezoid mnop using the origin as the center of dilation. which one of the following statements is true? a trapezoid mnop is dilated by a scale factor of 1/2 to create trapezoid mnop b trapezoid mnop is dilated by a scale factor of 1/2 to create trapezoid mnop c trapezoid mnop is dilated by a scale factor of 3 to create trapezoid mnop d trapezoid mnop is dilated by a scale factor of 2 to create trapezoid mnop

Explanation:

Step1: Select a point and its image

Let's take point M. Assume the coordinates of M are \((x_1,y_1)\) and of M' are \((x_2,y_2)\) from the graph. If M has coordinates \((2,8)\) and M' has coordinates \((1,4)\).

Step2: Calculate the scale - factor for x - coordinates

The scale - factor \(k\) for dilation with the origin as the center is given by \(k=\frac{x_2}{x_1}\). Here, \(k = \frac{1}{2}\).

Step3: Calculate the scale - factor for y - coordinates

Also, for the y - coordinates, \(k=\frac{y_2}{y_1}\). Since \(y_1 = 8\) and \(y_2=4\), \(k=\frac{4}{8}=\frac{1}{2}\).

Answer:

A. Trapezoid MNOP is dilated by a scale factor of \(\frac{1}{2}\) to create trapezoid M'N'O'P'