Question

1. graph the image of the quadrilateral below using a scale factor of k = 3/2. w (__, ) x (, ) y (, ) z (, __)

Explanation:

Step1: Assume original coordinates

Let the original coordinates of the vertices of the quadrilateral be \(W(x_1,y_1)\), \(X(x_2,y_2)\), \(Y(x_3,y_3)\), \(Z(x_4,y_4)\). Since the figure is not labeled with coordinates, for a general point \((x,y)\) in the original figure, the coordinates of its image \((x',y')\) after dilation with a scale - factor \(k = \frac{3}{2}\) are given by the formula \(x'=k\times x\) and \(y'=k\times y\).

Step2: Calculate new coordinates

For each vertex of the quadrilateral, if the original \(x\) - coordinate is \(x\) and the original \(y\) - coordinate is \(y\), the new \(x\) - coordinate \(x'=\frac{3}{2}x\) and the new \(y\) - coordinate \(y'=\frac{3}{2}y\). For example, if \(W\) has coordinates \((a,b)\), then \(W'\) has coordinates \((\frac{3}{2}a,\frac{3}{2}b)\). Without knowing the exact original coordinates from the graph, in general, for a point \((x,y)\) the new point after dilation with \(k = \frac{3}{2}\) is \((\frac{3}{2}x,\frac{3}{2}y)\).

Answer:

Without the original coordinates of \(W\), \(X\), \(Y\), \(Z\), we can only give the general form. If the original coordinates of \(W\) are \((x_W,y_W)\), \(X\) are \((x_X,y_X)\), \(Y\) are \((x_Y,y_Y)\), \(Z\) are \((x_Z,y_Z)\), then \(W'(\frac{3}{2}x_W,\frac{3}{2}y_W)\), \(X'(\frac{3}{2}x_X,\frac{3}{2}y_X)\), \(Y'(\frac{3}{2}x_Y,\frac{3}{2}y_Y)\), \(Z'(\frac{3}{2}x_Z,\frac{3}{2}y_Z)\)