Question

1. trapezoid j k l m was dilated to create the trapezoid j k l m shown on the grid. the scale factor used in the dilation was 2. daniel thinks the original point m was located at (-3,-3). donald thinks the original point m was located at (-12,-12). who was correct and why?

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated with a scale factor \(k\) from the origin, the new point is \((kx,ky)\).

Step2: Analyze Donald's claim

Donald says the original point \(M\) was \((- 3,-3)\). If the scale factor \(k = 2\), then the new point \(M'\) would be \((-3\times2,-3\times2)=(-6,-6)
eq(-12,-12)\)

Step3: Analyze Daniel's claim

Daniel says the original point \(M\) was \((-6,-6)\). If the scale factor \(k = 2\), then the new point \(M'\) would be \((-6\times2,-6\times2)=(-12,-12)\)

Answer:

Daniel was correct. When the original point \(M(-6,-6)\) is dilated with a scale factor \(k = 2\), using the formula \((x,y)\to(kx,ky)\), we get \(M'(-12,-12)\)