Error Analysis For the dilation with center (0,0) shown on the graph, your friend says the scale factor is (7)/(5) . What is the correct scale factor?What mistake did your friend likely make? B The correct scale factor is square

Step 1: Understand the concept of dilation in geometry. Dilation is a transformation that changes the size of a figure without altering its shape. The scale factor of a dilation is the ratio of the lengths of the sides of the image (the figure after the transformation) to the corresponding sides of the pre-image (the figure before the transformation).<br /><br />Step 2: Identify the corresponding points in the pre-image and the image. In this case, we can use points A and A', B and B', or C and C' because they correspond to each other in the two triangles.<br /><br />Step 3: Calculate the distance between the origin (0,0) and the corresponding points in the pre-image and the image. The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula √[(x2-x1)² + (y2-y1)²].<br /><br />For point A and A', the distance is the same (5 units) because they are at the same location.<br /><br />For point B and B', the distances are √[(-7-0)² + (0-0)²] = 7 units and √[(-5-0)² + (0-0)²] = 5 units respectively.<br /><br />For point C and C', the distances are √[(7-0)² + (-7-0)²] = √98 ≈ 9.9 units and √[(5-0)² + (-5-0)²] = √50 ≈ 7.1 units respectively.<br /><br />Step 4: Calculate the scale factor. The scale factor is the ratio of the distance from the origin to a point in the image to the corresponding distance in the pre-image. <br /><br />Using points B and B', the scale factor is 5/7.<br /><br />Using points C and C', the scale factor is √50/√98 ≈ 7.1/9.9 ≈ 0.717.<br /><br />The scale factors calculated using points B and B' and points C and C' are approximately the same, which indicates that the dilation is consistent.<br /><br />Step 5: Identify the mistake your friend made. Your friend likely made the mistake of inverting the ratio when calculating the scale factor. Instead of dividing the distance in the image by the distance in the pre-image (5/7), your friend divided the distance in the pre-image by the distance in the image (7/5).<br /><br />So, the correct scale factor is 5/7.