Answer:
The coordinates of the points of the rectangle A'B'C'D' are;
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = (2, -1)
Explanation:
Placing the point P as the origin of the chart, we have;
The coordinates of the points are given as follows;
The coordinates of the point B = (-4, 2)
The coordinates of the point C = (4, 2)
The coordinates of the point A = (-4, -2)
The coordinates of the point D = (4, -2)
Given that the sides are parallel to the axis, we have;
The length of the segment AB = 2 - (-2) = 4
The length of the segment BC = 4 - (-4) = 8
The length of the segment CD = 2 - (-2) = 4
The length of the segment AD = 4 - (-4) = 8
Therefore, a dilation by 1/2 will give;
The length of the segment A'B' = AB/2 = 4/2 = 2
The length of the segment B'C' = BC/2 = 8/2 = 4
The length of the segment C'D' = CD/2 = 4/2 = 2
The length of the segment A'D' = AD/2 = 8/2 = 4
The coordinates of the point A' = The coordinates of the point A/2 = (-4, -2)/2 = (-2, -1)
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = The coordinates of the point B/2 = (-4, 2)/2 = (-2, 1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = The coordinates of the point C/2 = (4, 2)/2 = (2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = The coordinates of the point D/2 = (4, -2)/2 = (2, -1)
The coordinates of the point D' = (2, -1).