Question

The endpoints of MN are M(2,5) and N(8, -1). Which shows the endpoints of the segment after it is translated along the vector (-2, 3)?

A) M(0, 8) and N(6, 2)
B) M(4, 2) and N(10, -4)
C) M(2, 8) and N(6, 2)
D) M(0, 2) and N(6, -4)

Answer 1

The new endpoints after translating the segment MN along the vector (-2, 3) are M(0, 8) and N(6, 2), which is option A.

Step-by-step explanation:

The student asked about the new endpoints of a line segment after it has been translated along a given vector. The vector for the translation is given as (-2, 3). This means that we need to subtract 2 from each x-coordinate and add 3 to each y-coordinate of the endpoints M(2,5) and N(8, -1).

To find the new coordinates for M after the translation, we calculate M'(2-2, 5+3), which gives us M'(0, 8). To find the new coordinates for N, we calculate N'(8-2, -1+3), which results in N'(6, 2).

Therefore, after the translation the new endpoints are M(0, 8) and N(6, 2), which corresponds to option A).