Question
Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C prime, has coordinates of (7.2, 3.6). What is the scale factor of the dilation and what are the coordinates of point A prime?
On a coordinate plane, triangle A B C has points (negative 3, 3), (1.5, 9), (6, 3). C prime is (7.2, 3.6).
The scale factor is 1.2 and the coordinates of point A prime are (–2.5, 2.5).
The scale factor is StartFraction 5 Over 6 EndFraction and the coordinates of point A prime are (–2.5, 2.5).
The scale factor is 1.2 and the coordinates of point A prime are (–3.6, 3.6).
The scale factor is StartFraction 5 Over 6 EndFraction and the coordinates of point A prime are (–3.6, 3.6).
On a coordinate plane, triangle A B C has points (negative 3, 3), (1.5, 9), (6, 3). C prime is (7.2, 3.6).
The scale factor is 1.2 and the coordinates of point A prime are (–2.5, 2.5).
The scale factor is StartFraction 5 Over 6 EndFraction and the coordinates of point A prime are (–2.5, 2.5).
The scale factor is 1.2 and the coordinates of point A prime are (–3.6, 3.6).
The scale factor is StartFraction 5 Over 6 EndFraction and the coordinates of point A prime are (–3.6, 3.6).
Answers
GPT-4o mini
To determine the scale factor of dilation from triangle ABC to its image triangle A'B'C', we can use the coordinates of point C and its corresponding point C'.
The coordinates of point C are (6, 3) and the coordinates of C' are (7.2, 3.6).
We can calculate the scale factor \( k \) using the formula:
\[
k = \frac{\text{Coordinate of C'}}{\text{Coordinate of C}}
\]
Calculating for both the x and y coordinates:
1. For the x-coordinate:
\[
k = \frac{7.2}{6} = 1.2
\]
2. For the y-coordinate:
\[
k = \frac{3.6}{3} = 1.2
\]
Since both coordinates give the same scale factor, the scale factor of the dilation is \( k = 1.2 \).
Next, to find the coordinates of A' given the coordinates of point A (which are (-3, 3)), we can multiply each coordinate of A by the scale factor:
\[
A' = (x \cdot k, y \cdot k) = (-3 \cdot 1.2, 3 \cdot 1.2) = (-3.6, 3.6)
\]
Thus, the coordinates of point A' are (-3.6, 3.6).
Putting it all together:
- The scale factor is \( 1.2 \).
- The coordinates of point A' are (-3.6, 3.6).
So the correct choice is:
**The scale factor is 1.2 and the coordinates of point A prime are (-3.6, 3.6).**
The coordinates of point C are (6, 3) and the coordinates of C' are (7.2, 3.6).
We can calculate the scale factor \( k \) using the formula:
\[
k = \frac{\text{Coordinate of C'}}{\text{Coordinate of C}}
\]
Calculating for both the x and y coordinates:
1. For the x-coordinate:
\[
k = \frac{7.2}{6} = 1.2
\]
2. For the y-coordinate:
\[
k = \frac{3.6}{3} = 1.2
\]
Since both coordinates give the same scale factor, the scale factor of the dilation is \( k = 1.2 \).
Next, to find the coordinates of A' given the coordinates of point A (which are (-3, 3)), we can multiply each coordinate of A by the scale factor:
\[
A' = (x \cdot k, y \cdot k) = (-3 \cdot 1.2, 3 \cdot 1.2) = (-3.6, 3.6)
\]
Thus, the coordinates of point A' are (-3.6, 3.6).
Putting it all together:
- The scale factor is \( 1.2 \).
- The coordinates of point A' are (-3.6, 3.6).
So the correct choice is:
**The scale factor is 1.2 and the coordinates of point A prime are (-3.6, 3.6).**