Question

△abc is the image of △abc after a dilation by a scale factor of 5/2, with the origin as the center of dilation. plot and label triangle △abc. > use the graphing tool to plot and label the triangle. polygon label move undo redo × reset

Explanation:

Step1: Recall dilation formula

If the center of dilation is the origin \((0,0)\) and the scale - factor is \(k\), and a point \((x,y)\) in the original figure is dilated to a point \((x',y')\) in the image, then \(x'=kx\) and \(y' = ky\). Here \(k=\frac{5}{2}\).

Step2: Identify coordinates of \(\triangle ABC\)

From the graph, assume \(A(- 4,2)\), \(B(3,2)\), \(C(3,-4)\).

Step3: Calculate coordinates of \(A'\)

For point \(A(-4,2)\), \(x'_A=\frac{5}{2}\times(-4)=-10\), \(y'_A=\frac{5}{2}\times2 = 5\), so \(A'(-10,5)\).

Step4: Calculate coordinates of \(B'\)

For point \(B(3,2)\), \(x'_B=\frac{5}{2}\times3=\frac{15}{2}=7.5\), \(y'_B=\frac{5}{2}\times2 = 5\), so \(B'(7.5,5)\).

Step5: Calculate coordinates of \(C'\)

For point \(C(3,-4)\), \(x'_C=\frac{5}{2}\times3 = 7.5\), \(y'_C=\frac{5}{2}\times(-4)=-10\), so \(C'(7.5,-10)\).

Step6: Plot the points

Plot the points \(A'(-10,5)\), \(B'(7.5,5)\) and \(C'(7.5,-10)\) on the graph and label them as \(A'\), \(B'\) and \(C'\) respectively to form \(\triangle A'B'C'\).

(Note: Since this is a graph - based problem, the actual plotting should be done on the provided graphing tool. The above steps give the coordinates of the vertices of the dilated triangle.)

Answer:

Plot \(A'(-10,5)\), \(B'(7.5,5)\) and \(C'(7.5,-10)\) and label them to form \(\triangle A'B'C'\) on the graphing tool.