Question

question 1 - 4
triangle abc is transformed to create triangle mno and triangle pqr as described below.
. mno represents the translation 2 units left and 2 units down of triangle abc.
. pqr represents the dilation of triangle abc by a scale factor of 2.
which of these is correct?
the transformation of abc to pqr preserves both the side lengths and angle measures of the triangle
the transformation of abc to mno preserves both the side lengths and angle measures of the triangle
the transformation of abc to pqr preserves the side lengths but not the angle measures of the triangle
the transformation of abc to mno preserves the angle measures but not the side lengths of the triangle

Explanation:

Step1: Recall properties of translation

Translation is a rigid - motion. It moves every point of a figure the same distance in the same direction. It preserves side lengths and angle measures.

Step2: Recall properties of dilation

Dilation changes the size of a figure by a scale factor. If the scale factor is \(k
eq1\), side lengths are multiplied by \(k\). Angle measures are preserved in dilation. When dilating \(\triangle ABC\) by a scale factor of 2 to get \(\triangle PQR\), side lengths of \(\triangle PQR\) are twice those of \(\triangle ABC\), but angle measures are the same. When translating \(\triangle ABC\) 2 units left and 2 units down to get \(\triangle MNO\), both side lengths and angle measures are preserved.

Answer:

The transformation of ABC to MNO preserves both the side lengths and angle measures of the triangle.