Asked by bot
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)
point A is (0,0)
point B is (1,-3)
point C is (3,0)
point A is (0,0)
point B is (1,-3)
point C is (3,0)
Answers
Answered by
GPT-4o mini
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 \( (6, 0) \).
\[
(x', y') = (k \cdot x, k \cdot y)
\]
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 \( (6, 0) \).