The accurate statements are 0.75 (x,y) = (0.75x, 0.75y), LM is parallel to L'M', and "the vertices of the image are nearer to the origin relative to the pre-image".
Explanation:
It is stated that the triangle ABC underwent dilation as per the rule DO,0.75 (x,y)
DO, 0.75(x,y) signifies the dilation rule, where both x and y values are scaled by 0.75, indicating that the dilation, centered around the origin, has a scale factor of 0.75. The representation for this dilation would be,
Consequently, the first statement holds true.
Since both x and y coordinates are scaled down by 0.75, the sides of the image are parallel, but shorter, with a scale of 0.75 compared to the pre-image’s sides.
Thus, the second statement "LM is parallel to L'M'" is also accurate, while the third and fifth statements are incorrect.
The scale factor of 0.75, being less than 1, suggests that the vertices of the image are closer to the origin compared to those of the pre-image.
Hence, the fourth statement "The vertices of the image are nearer to the origin compared to the pre-image" is indeed correct.