Question

is trapezoid abdc the result of a dilation of trapezoid mnpq by a scale factor of \\( \frac { 2 } { 5 } \\)? why or why not?
yes, because ab and cd are each \\( \frac { 2 } { 5 } \\) the lengths mn and qp.
yes, because sides ab and cd are parallel to sides mn and qp.
no, because ab is \\( \frac { 2 } { 5 } \\) the length mn but cd is \\( \frac { 1 } { 1 } \\) the length qp.
no, because sides ab and cd have different slopes from sides mn and qp.

Explanation:

Step1: Calculate the length of AB and MN

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for horizontal lines (where \(y_1=y_2\)), if \(A(-1,1)\), \(B(1,1)\), then \(AB=\vert1 - (- 1)\vert=2\). If \(M(-4,2)\), \(N(4,2)\), then \(MN=\vert4-(-4)\vert = 8\). And \(\frac{AB}{MN}=\frac{2}{8}=\frac{1}{4}
eq\frac{2}{5}\)

Step2: Calculate the length of CD and QP

If \(C(-1,-1)\), \(D(1,-1)\), then \(CD = \vert1-(-1)\vert=2\). If \(Q(-4,-3)\), \(P(4,-3)\), then \(QP=\vert4 - (-4)\vert=8\). And \(\frac{CD}{QP}=\frac{2}{8}=\frac{1}{4}
eq\frac{2}{5}\)

Answer:

C. No, because AB is \(\frac{1}{4}\) the length MN but CD is \(\frac{1}{4}\) the length QP.