Question

The triangle with vertices O(-3,3), M(-1, 3), and G(-3, 0) is dilated with a scale factor k = 2 and then translated (x, y) -> (x + 5, y - 1). Find the coordinates of O (after the two transformations).

Answer 1

After a dilation with a scale factor of 2 and a translation of (x + 5, y - 1), the coordinates of point O change from (-3,3) to (-1,5).

Step-by-step explanation:

The student's question involves finding the coordinates of point O after it undergoes a dilation and a translation. Initially, O is at (-3,3).

1. First, we apply dilation with a scale factor of k = 2. The coordinates of O after dilation become:

O(-3 × 2, 3 × 2) = O(-6, 6).

1. Next, we apply the translation (x, y) -> (x + 5, y - 1). The coordinates of O after translation become:

O(-6 + 5, 6 - 1) = O(-1, 5).

Therefore, after the two transformations, the coordinates of point O become (-1, 5).