Find the coordinates of point C' by dilating triangle ABC by a scale factor of 2 with a center of dilation at the origin. Enter your response as an ordered pair.

Question

Coordinate A (0,0)
Coordinate B (1,-3)
Coordinate C (3,0)

Answer 1

To find the coordinates of point C' after dilating triangle ABC by a scale factor of 2 with the center of dilation at the origin (0,0), we can use the following formula for dilation:

If \( (x, y) \) are the coordinates of a point before dilation, then the coordinates after dilation will be given by:

\[ (x', y') = (kx, ky) \]

where \( k \) is the scale factor.

For triangle ABC:

• Coordinate A is \( (0,0) \)
• Coordinate B is \( (1,-3) \)
• Coordinate C is \( (3,0) \)

Since we are only interested in point C (which has coordinates \( (3,0) \)), we will apply the dilation to C:

1. Scale factor \( k = 2 \)
2. Original coordinates of point C: \( (3, 0) \)

Now applying the dilation formula: \[ C' = (2 \cdot 3, 2 \cdot 0) = (6, 0) \]

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

The final answer is: \[ \boxed{(6, 0)} \]