In the following graph we observe line segment AB being mapped by translation to line segment A'B'. A. In two or more sentences, explain what test you could perform to check the validity of this translation. B. Prove mathematically that the translation is valid using the test you mentioned above.

(b)

Step-by-step explanation:

Part A

When a line segment goes under translation, the pre-image and the image are have the same length.

Therefore, to check if A'B' is a valid translation of AB, we determine the length of both line segments and compare.

Part B

Similarly

Since , we can conclude that the translation of AB to A'B' is valid.

tangent

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.