Find the coordinates of point C′ by dilating ΔABC by a scale factor of 2 with a center of dilation at the origin. Enter your response as an ordered pair. (1 point)

Question

point A is (0,0)
point B is (1,-3)
point C is (3,0)

Answer 1

To find the coordinates of point \( C' \) after dilating triangle \( \Delta ABC \) by a scale factor of 2 with the center of dilation at the origin, we can use the following formula for dilating a point \( (x, y) \):

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \( k \) is the scale factor. In this case, \( k = 2 \).

Point \( C \) has the coordinates \( (3, 0) \).

Using the dilation formula:

\[ C' = (2 \cdot 3, 2 \cdot 0) = (6, 0) \]

Thus, the coordinates of point \( C' \) are \( (6, 0) \).