Question

select the correct answer from each drop - down menu.
triangle abc is shown in the coordinate plane. it is translated 6 units left and 4 units down. then it is dilated by a scale factor of 3 origin. complete the statements.
the translation of triangle abc the dilation of triangle abc preserves angles but not side lengths preserves side lengths and angles does not preserve side lengths and angles preserves side lengths but not angles

Explanation:

Step1: Recall properties of translation

Translation is a rigid transformation. Rigid transformations preserve side - lengths and angles. So, the translation of triangle \(ABC\) preserves side lengths and angles.

Step2: Recall properties of dilation

Dilation is a non - rigid transformation. A dilation with a scale factor \(k
eq1\) changes the side - lengths (by a factor of \(k\)). But angles are preserved in a dilation because the shape of the figure remains the same in terms of the measure of angles. So, the dilation of triangle \(ABC\) preserves angles but not side lengths.

Answer:

The translation of triangle \(ABC\): preserves side lengths and angles; The dilation of triangle \(ABC\): preserves angles but not side lengths.