Suppose a dilation of ΔUVW by scale factor of 1/4, centered at the origin. Which new vertices are correct? Choose all that are correct
a
U′(−2, −1)
b
U′(−1, −2)
c
V′(1, −1)
d
V′(−1, 1)
e
W′(−2, 2)
I believe the answer is E. W'(-2, 2)
no
To find the new vertices after a dilation of ΔUVW by a scale factor of 1/4 centered at the origin, you can multiply the coordinates of each vertex by the scale factor.
Given that the vertices of the original triangle are U(1, 2), V(3, 4), and W(5, 6), we can calculate the new vertices as follows:
U′ = (1/4) * U = (1/4) * (1, 2) = (1/4, 1/2)
V′ = (1/4) * V = (1/4) * (3, 4) = (3/4, 1)
W′ = (1/4) * W = (1/4) * (5, 6) = (5/4, 3/2)
Now, let's check which of the given options match the calculated new vertices:
a) U′(-2, -1): This does not match the calculated new vertex (1/4, 1/2).
b) U′(-1, -2): This does not match the calculated new vertex (1/4, 1/2).
c) V′(1, -1): This does not match the calculated new vertex (3/4, 1).
d) V′(-1, 1): This does not match the calculated new vertex (3/4, 1).
e) W′(-2, 2): This does not match the calculated new vertex (5/4, 3/2).
None of the given options match the calculated new vertices, so none of the options are correct.
f
W′(2, −2)
a, c, e, f