Question

parallelogram mnpq was dilated to create parallelogram mnpq
which statements are true about the parallelograms? select three options
the length of side mn is 2 units
the length of side mn is 5 units
the image is smaller than the pre - image
sides mq and mq both have the same slope, 1
the scale factor is \\( \frac { 2 } { 5 } \\)

Explanation:

Step1: Calculate the length of \(MN\)

Using the distance formula for horizontal line (since \(M\) and \(N\) have the same \(y -\)coordinate). If \(M=(2,-2)\) and \(N=(4,-2)\), then \(MN=\vert4 - 2\vert=2\) units.

Step2: Calculate the length of \(M'N'\)

If \(M'=(5,-5)\) and \(N'=(10,-5)\), then \(M'N'=\vert10 - 5\vert = 5\) units.

Step3: Calculate the slope of \(MQ\) and \(M'Q'\)

For \(MQ\): \(M=(2,-2)\), \(Q=(1,-4)\). Slope \(m=\frac{-4+2}{1 - 2}=\frac{-2}{-1}=1\).
For \(M'Q'\): \(M'=(5,-5)\), \(Q'=(3,-7)\). Slope \(m=\frac{-7 + 5}{3-5}=\frac{-2}{-2}=1\).

Step4: Check the scale - factor

The scale factor \(k=\frac{M'N'}{MN}=\frac{5}{2}\), so the image is larger than the pre - image (not smaller), and the scale factor is \(\frac{5}{2}\) (not \(\frac{2}{5}\)).

Answer:

• The length of side \(MN\) is \(2\) units.
• The length of side \(M'N'\) is \(5\) units.
• Sides \(MQ\) and \(M'Q'\) both have the same slope, \(1\).