We are given a transformation of a triangle and we are asked the following questions:
a) The figure was translated from Quadrant 1 to Quadrant 3. To answer this question let's remember the numeration of quadrants in a plane.
Therefore, it is false that the triangle was translated from quadrant 1 to quadrant 3. It was translated from quadrant 3 to quadrant 1.
b) The translation can be represented by (x + 8, y + 7): We can see from the graph that the translation is done by moving each point 7 units to the right and 8 units upwards, therefore the transformation is (x', y') = (x + 7, y + 8). Therefore, the statement is false.
c) the orientation of the figure did not change: Since the transformation is just a translation, and translation does not change orientation then the statement is true.
d) The pre-image are congruent: Since translations do not change the distance between points and the angles remain the same, the two triangles are congruent.
e) The orientation of the vertices changed.: Since translations do not change orientation then the orientation of the vertices is the same. The statement is true.