Question

draw a new figure that has been dilated by a factor of 1/2. (centered at the origin).

Explanation:

Step1: Identify vertex coordinates

Let's assume the coordinates of the vertices of the original figure are \(A(0,0)\), \(B(x_1,y_1)\), \(C(x_2,y_2)\), \(D(x_3,0)\). For dilation centered at the origin with a scale - factor \(k = \frac{1}{2}\), the formula for the coordinates of the dilated points \((x',y')\) from the original points \((x,y)\) is \(x'=k\times x\) and \(y'=k\times y\).

Step2: Calculate dilated coordinates

For point \(B(x_1,y_1)\), the dilated point \(B'\) has coordinates \((\frac{1}{2}x_1,\frac{1}{2}y_1)\). For point \(C(x_2,y_2)\), the dilated point \(C'\) has coordinates \((\frac{1}{2}x_2,\frac{1}{2}y_2)\). Point \(A(0,0)\) remains at \((0,0)\) after dilation (\(\frac{1}{2}\times0 = 0\)), and for point \(D(x_3,0)\), the dilated point \(D'\) has coordinates \((\frac{1}{2}x_3,0)\).

Step3: Draw the new figure

Plot the dilated points \(A'\), \(B'\), \(C'\), \(D'\) on the same coordinate - grid and connect them in the same order as the original figure to get the dilated figure.

Answer:

Draw the figure with vertices obtained by dilating the original vertices by a factor of \(\frac{1}{2}\) centered at the origin.