Suppose the parallelogram on the coordinate plane is dilated in reference to the origin using a magnitude of 3. What would be the coordinates of the new vertices of E′F′G′H ?
1.)E'(2,8), F'(5,11), G'(7,7), and H'(4,4)
2.)E'(-3,15) F'(6,24), G'(12,12), and H'(3,3)
3.)E'(-4,2), F'(-1,5), G'(1,1), and H'(-2,-2)
4.)E'(-1/3,5/3), F'(2/3,8/3), G'(4/3,4/3), and H'(1/3,1/3)
To dilate a point in reference to the origin, we multiply each coordinate of the point by the scale factor. In this case, the scale factor is 3.
For option 1, if we multiply each coordinate by 3, we get:
E' = (2*3, 8*3) = (6, 24)
F' = (5*3, 11*3) = (15, 33)
G' = (7*3, 7*3) = (21, 21)
H' = (4*3, 4*3) = (12, 12)
These coordinates do not match the given coordinates in option 1.
For option 2, if we multiply each coordinate by 3, we get:
E' = (-3*3, 15*3) = (-9, 45)
F' = (6*3, 24*3) = (18, 72)
G' = (12*3, 12*3) = (36, 36)
H' = (3*3, 3*3) = (9, 9)
These coordinates do not match the given coordinates in option 2.
For option 3, if we multiply each coordinate by 3, we get:
E' = (-4*3, 2*3) = (-12, 6)
F' = (-1*3, 5*3) = (-3, 15)
G' = (1*3, 1*3) = (3, 3)
H' = (-2*3, -2*3) = (-6, -6)
These coordinates do not match the given coordinates in option 3.
For option 4, if we multiply each coordinate by 3, we get:
E' = (-1/3*3, 5/3*3) = (-1, 5)
F' = (2/3*3, 8/3*3) = (2, 8)
G' = (4/3*3, 4/3*3) = (4, 4)
H' = (1/3*3, 1/3*3) = (1, 1)
These coordinates match the given coordinates in option 4.
Therefore, the coordinates of the new vertices of E'F'G'H' would be E'(-1, 5), F'(2, 8), G'(4, 4), and H'(1, 1), which is option 4.