The vertices of a trapezoid are shown below.

Question

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)

Answer 1

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)