Question

part a: what are the coordinates of the third point of the triangle after the translation? (3,3) (5,1) (5,3) (3,1) part b: describe the transformation that would map the pre - image to the image algebraically. (x,y) -> (2x,y) (x,y) -> (x,y + 2) (x,y) -> (x + 2,y) (x,y) -> (x + 2,y + 2)

Explanation:

Step1: Analyze Part A

Since no pre - translation coordinates are given, we assume we are just checking the options based on some unshown context. But if we consider general transformation concepts, we need to analyze the options for the third - point coordinates.

Step2: Analyze Part B

For a translation in the coordinate plane, if we have a transformation of the form $(x,y)\to(x + a,y + b)$, $a$ represents the horizontal shift and $b$ represents the vertical shift.

• For $(x,y)\to(2x,y)$ is a horizontal stretch by a factor of 2.
• For $(x,y)\to(x,y + 2)$ is a vertical shift up by 2 units.
• For $(x,y)\to(x + 2,y)$ is a horizontal shift right by 2 units.
• For $(x,y)\to(x + 2,y+2)$ is a shift right by 2 units and up by 2 units.

Answer:

Part A: Since no pre - translation information is given, we assume the selected option (5,1) is correct based on the problem context. So the answer is (5,1).
Part B: A translation that moves a point 2 units to the right (in the x - direction) and no vertical movement is represented by $(x,y)\to(x + 2,y)$. So the answer is $(x,y)\to(x + 2,y)$.