Question

32:51

On a coordinate plane, trapezoids A B D C and M N P Q are shown. The length of A B is 4 units and the length of B D is 2 units. The length of M N is 10 units and the length of N P is 6 units.

Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of Two-fifths? Why or why not?

Yes, because AB and CD are each Two-fifths the lengths MN and QP.
Yes, because sides AB and CD are parallel to sides MN and QP.
No, because AB is Two-fifths the length MN but CD is One-third the length QP.
No, because sides AB and CD have different slopes from sides MN and QP.

Answer 1

c

Explanation:

Answer 2

9514 1404 393

Answer:

C. No, because AB is Two-fifths the length MN but CD is One-third the length QP.

Explanation:

Dilation multiplies each coordinate or length by the scale factor. Here, different corresponding lengths are multiplied by different values, so no dilation is involved.

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Additional comment

Dilation shouldn't change any slopes, so if slopes of corresponding segments are different, that is another indication dilation is not involved. (No figure is supplied here, so we cannot judge slopes.)