Question

7.
which is a true statement about the transformation?
○ the pre - image is in quadrant ii.
○ the orientation of the vertices was changed.
○ triangle abc was translated 8 units left and 3 units up.
○ the orientation of the figure was changed.

Explanation:

Step1: Analyze Quadrant of Pre - image

The pre - image (triangle ABC) has vertices with negative x - coordinates and positive y - coordinates (e.g., point B is at (- 6, 3), point A is at (- 6, 7), point C is at (- 2, 3)). Quadrant II is defined as the set of points where \(x<0\) and \(y > 0\). So the pre - image is in Quadrant II.

Step2: Analyze Orientation Change

A translation is a rigid transformation. In a translation, the orientation of the figure (the order of the vertices, clockwise or counter - clockwise) and the orientation of the vertices do not change. So the options about the orientation being changed are incorrect.

Step3: Analyze Translation Direction and Distance

To find the translation, we can look at the change in coordinates of a vertex. Let's take point B (- 6, 3) and its image \(B'\) (2, 0). The change in x - coordinate is \(2-(-6)=8\) (so it is a translation 8 units to the right), and the change in y - coordinate is \(0 - 3=- 3\) (a translation 3 units down). So the option about translating 8 units left and 3 units up is incorrect.

Answer:

The pre - image is in Quadrant II.