Final Answer:
a. After the transformation, the coordinates of the vertices are: N(-1,0), U(1,5), L(3,2), H(1,-2)
b. After the transformation, the coordinates of the vertices are: N(1,0), U(3,5), L(5,2), H(3,-2)
c. After the transformation, the coordinates of the vertices are: N(0,-2), U(2,3), L(4,0), H(2,-4)
d. After the transformation, the coordinates of the vertices are: N(1,-1), U(3,4), L(5,1), H(3,-3)
Step-by-step explanation:
In each case, the transformation involves a shift or translation in the x and y directions. Let's break down the transformations:
a. The figure is shifted one unit to the left (x-coordinate decreases by 1) and remains unchanged along the y-axis.
b. The figure is shifted two units to the right (x-coordinate increases by 2) and remains unchanged along the y-axis.
c. The figure is shifted two units downward (y-coordinate decreases by 2) and remains unchanged along the x-axis.
d. The figure is shifted one unit upward (y-coordinate increases by 1) and remains unchanged along the x-axis.
Transformations in geometry involve changes to the position, size, or orientation of figures. In this case, we focused on translations, where the figures are shifted without any change in shape or orientation. Understanding different types of transformations is crucial in geometry and its applications.