Thangle RST has vertices
R(1, 0), S(-1, 1), and T(1, -6). Triangle RST
is dilated by a scale factor of 4.5 with the
origin as the center of dilation. What are the
new coordinates of the vertices of R'ST?
A R'(4.5, 0), S'(-4.5, 4.5), T (4.5, 0)
B R(-4.5, 0), S' (4.5, 4.5), T(4.5, 0)
C R (4.5, 0), (-4.5, 4.5), T(-4.5, 0)
D R'(-4.5, 0), S'(-4.5, 4.5), T (4.5, -27)
To dilate a point by a scale factor of 4.5 with the origin as the center of dilation, we simply multiply the coordinates of the point by the scale factor.
The new coordinates of R' can be found by multiplying the coordinates of R(1, 0) by 4.5:
R' = (1 * 4.5, 0 * 4.5) = (4.5, 0)
The new coordinates of S' can be found by multiplying the coordinates of S(-1, 1) by 4.5:
S' = (-1 * 4.5, 1 * 4.5) = (-4.5, 4.5)
The new coordinates of T' can be found by multiplying the coordinates of T(1, -6) by 4.5:
T' = (1 * 4.5, -6 * 4.5) = (4.5, -27)
Therefore, the new coordinates of the vertices of R'ST are:
R'(4.5, 0), S'(-4.5, 4.5), T(4.5, -27)
The correct answer is option D.