Final answer:
The segment with endpoints P(4, -6) and L(-2, 1) is translated using the mapping (x, y) = (x + 5, y). P' is found by adding 5 to the x-coordinate of P, resulting in P'(9, -6), and L' is found by adding 5 to the x-coordinate of L, resulting in L'(3, 1). The correct answer is option c.
Step-by-step explanation:
The student's question is about the translation of a line segment in the Cartesian coordinate system using a given mapping. The line segment has endpoints P(4, -6) and L(-2, 1). The mapping to be used for the translation is (x, y) = (x + 5, y), which means each x-coordinate of the endpoints should be increased by 5 units, while the y-coordinate remains the same.
To find the translated coordinates of point P, known as P', we add 5 to the x-coordinate of P to get P'(4 + 5, -6) which is P'(9, -6). To find the translated coordinates of point L, known as L', we add 5 to the x-coordinate of L to get L'(-2 + 5, 1) which is L'(3, 1). Therefore, the coordinates of points P' and L' after the segment translation are P'(9, -6) and L'(3, 1), respectively. The correct answer is option c. P'(9,-6), L'(3, 1).