Question

Triangle PQR was translated using the rule (x−2,y+5) and then dilated by a scale factor of 3 to create triangle P" Q′′ R′′ . Which statement explains why the triangles are similar?

a. Translations and dilations preserve orientation; therefore, the corresponding angles of PQR and P"Q′′R" are proportional.
b. Translations and dilations preserve side length; therefore, the corresponding sides of PQR and PQ′′R'' are congruent.
c. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of PQR are proportional.
d. Translations and dilations preserve collinearity; therefore, the corresponding sides of PQR and P ′′Q′′R′′ are congruent.

Answer 1

The correct statement is that translations and dilations preserve the orientation and proportionality of the sides, making the triangles similar with proportional corresponding angles.

Step-by-step explanation:

The statement that explains why triangles PQR and P"Q"R" are similar is that translations and dilations preserve angular measure and proportionality of sides, but not necessarily their length. Specifically, the answer is (a): Translations and dilations preserve orientation; therefore, the corresponding angles of PQR and P"Q"R" are proportional. A translation does not change the shape or angles of a triangle, it just moves it to a different location. A dilation increases or decreases the size of the triangle by a constant scale factor, which means all sides are multiplied by the same amount, maintaining their proportionality.