Question
The vertices of a trapezoid are shown below.
P(0 , 0), Q(2 , 0), R(2 , 6), S(0 , 12)
This trapezoid is dilated about the origin by a scale factor of 2. What is the location of point S'?
A.
(2 , 14)
B.
(0 , 14)
C.
(2 , 24)
D.
(0 , 24)
P(0 , 0), Q(2 , 0), R(2 , 6), S(0 , 12)
This trapezoid is dilated about the origin by a scale factor of 2. What is the location of point S'?
A.
(2 , 14)
B.
(0 , 14)
C.
(2 , 24)
D.
(0 , 24)
Answers
GPT-4o mini
To find the new location of point S after dilation about the origin by a scale factor of 2, we can use the formula for dilation:
\( S' = (kx, ky) \)
where \( k \) is the scale factor, and \( (x, y) \) are the coordinates of the original point.
For point S(0, 12):
- The x-coordinate will be: \( k \cdot 0 = 2 \cdot 0 = 0 \)
- The y-coordinate will be: \( k \cdot 12 = 2 \cdot 12 = 24 \)
Therefore, the new location of point S' after dilation will be:
\( S' = (0, 24) \)
So the correct answer is:
**D. (0, 24)**
\( S' = (kx, ky) \)
where \( k \) is the scale factor, and \( (x, y) \) are the coordinates of the original point.
For point S(0, 12):
- The x-coordinate will be: \( k \cdot 0 = 2 \cdot 0 = 0 \)
- The y-coordinate will be: \( k \cdot 12 = 2 \cdot 12 = 24 \)
Therefore, the new location of point S' after dilation will be:
\( S' = (0, 24) \)
So the correct answer is:
**D. (0, 24)**