Question

Triangle ABC is dilated by a scale factor of 2 with a center of dilation at the origin. What are the coordinates of the image of point C prime?

On a coordinate plane, triangle A B C has points (1, 1), (1.5, 3), (2, 1).
(2, 4)
(4, 2)
(One-half, 1)
(1, one-half)

Answer 1

To find the coordinates of point C' after the dilation of triangle ABC by a scale factor of 2 with the center of dilation at the origin, we first need the coordinates of point C in triangle ABC.

Given the coordinates of the points:
- A (1, 1)
- B (1.5, 3)
- C (2, 1)

The coordinates of point C are (2, 1).

The formula for dilating a point \( (x, y) \) by a scale factor \( k \) with respect to the origin is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
Here, the scale factor \( k \) is 2, so we substitute \( x = 2 \) and \( y = 1 \) into the formula:

\[
x' = 2 \cdot 2 = 4
\]
\[
y' = 2 \cdot 1 = 2
\]

Thus, the coordinates of the image of point C prime (C') after the dilation are \( (4, 2) \).

Therefore, the answer is:
**(4, 2)**.