Question

Which algebraic rule describes the translation based on the given coordinates?

Cordinates: RUST: R= -4,-1 U= -4,-3 S= -1,-1 T= -1,-3
Cordinates: R'U'S'T': R'= 4,1 U'= 4,3 S'= 1,1 T'= 1,3
A) Translation by 8 units to the right and 4 units up
B) Translation by 4 units to the left and 2 units down
C) Reflection across the y-axis
D) Rotation by 90 degrees counterclockwise

Answer 1

The algebraic transformation that maps the given coordinates is a translation by 8 units to the right and 2 units up, as each point's x coordinate increased by 8 and the y coordinate increased by 2.

Step-by-step explanation:

To determine the type of transformation that maps points R(-4,-1), U(-4,-3), S(-1,-1), T(-1,-3) to points R'(4,1), U'(4,3), S'(1,1), T'(1,3), we can calculate the changes in the x and y coordinates from the original points to their corresponding points after transformation.

We can see that for point R to move from (-4,-1) to (4,1), the x coordinate increased by 8 units (c. Horizontally to the right side of the coordinate system) and the y coordinate increased by 2 units (a. Vertically upward in the coordinate system). The same change in coordinates applies to the other points as well. This transformation is a translation because each point moves the same distance in the same direction.

Therefore, the algebraic rule that describes this translation is A) Translation by 8 units to the right and 2 units up.