Question: User: WHICH ONE IS CORRECT: A, B, C, OR D? HURRY UP Question 2 (1 point) (02.01 HC) Triangle JOY is translated using the rule $ (x, y) \to (x + 3, y - 2) $ to create triangle $ J' O' Y' $. If a line segment is drawn from point $ J $ to point $ J' $ and from point $ O $ to point $ O' $, which statement would best describe the line segments drawn? a They share the same midpoints. b They create diameters of concentric circles. c They are parallel and congruent. d They are perpendicular to each other.

1. **State the problem:** Triangle $JOY$ is translated by the rule $$ (x, y) \to (x + 3, y - 2) $$ to form triangle $J'O'Y'$. We draw line segments from $J$ to $J'$ and from $O$ to $O'$. We need to determine which statement best describes these line segments. 2. **Understand the translation:** The translation rule moves every point by adding $3$ to the $x$-coordinate and subtracting $2$ from the $y$-coordinate. 3. **Analyze the line segments $JJ'$ and $OO'$:** - The segment $JJ'$ connects $J(x, y)$ to $J'(x+3, y-2)$. - The segment $OO'$ connects $O(x, y)$ to $O'(x+3, y-2)$. 4. **Calculate the vector representing these segments:** The vector from $J$ to $J'$ is $$ \vec{v} = (3, -2) $$. Similarly, the vector from $O$ to $O'$ is also $$ \vec{v} = (3, -2) $$. 5. **Determine properties of the segments:** - Both segments have the same direction vector, so they are parallel. - Both segments have the same length, calculated by $$ \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} $$, so they are congruent. 6. **Check other options:** - They do not share midpoints because $J$ and $O$ are different points. - They do not create diameters of concentric circles; no circles are involved. - They are not perpendicular because the direction vector is the same for both. **Final answer:** **c. They are parallel and congruent.**