1. A graph of triangle GHJ and its image after a dilation by a scale factor of 0.25 centered at the origin (0, 0) is shown below.
2. Yes, the dilation is a reduction because the image of triangle GHJ is smaller.
In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size (dimensions) of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image (triangle GHJ) by applying a scale factor of 0.25 that is centered at the origin in order to produce the coordinates of its image as follows:
Ordered pair G (-2, -2) → Ordered pair G' (-2 × 0.25, -2 × 0.25) = Ordered pair G' (-0.5, -0.5).
Ordered pair H (-2, 6) → Ordered pair H' (-2 × 0.25, 6 × 0.25) = Ordered pair H' (-0.5, 1.5).
Ordered pair J (2, 6) → Ordered pair J' (2 × 0.25, 6 × 0.25) = Ordered pair J' (0.5, 1.5).
In concluson, we can logically deduce that the dilation is a reduction because the size of the pre-image is larger than the image.
Complete Question:
The vertices of a figure are given. Draw the figure and its image after a dilation with the given scale factor. Then identify the type of dilation. G(-2,-2), H(-2, 6), J(2, 6) ; k=0.25