The vertices of pentagon LMPQR are at L(4, -2), M(5, -2), P(8, -5), Q(6, -7), R(2, -4). The coordinates of the pentagon after two translations are L'(-5, -1), M'(-4, -1), P'(-1, -4), Q'(-3, -6), R'(-7, -3).

How was LMPQR translated to create L'M'P'Q'R'?

To the left by 9 units and 1 unit up
To the right by 9 units and 1 unit up
To the left by 1 unit and 9 units up
To the right by 1 unit and 9 units up

compare any of the original points and it image point

e.g. L(4,-2) ----> L'(-5,-1)
didn't the x move 9 units to the left, and the y moved 1 unit up ?
mmmhhh?

test it for the other points

To determine how the pentagon LMPQR was translated to create L'M'P'Q'R', we can compare the coordinates of each vertex before and after the translation.

The x-coordinate of each vertex in L'M'P'Q'R' is obtained by subtracting 9 from the x-coordinate in LMPQR. The y-coordinate of each vertex in L'M'P'Q'R' is obtained by adding 1 to the y-coordinate in LMPQR.

Let's go through each vertex:

L:
- The x-coordinate of L' is 4 - 9 = -5
- The y-coordinate of L' is -2 + 1 = -1

M:
- The x-coordinate of M' is 5 - 9 = -4
- The y-coordinate of M' is -2 + 1 = -1

P:
- The x-coordinate of P' is 8 - 9 = -1
- The y-coordinate of P' is -5 + 1 = -4

Q:
- The x-coordinate of Q' is 6 - 9 = -3
- The y-coordinate of Q' is -7 + 1 = -6

R:
- The x-coordinate of R' is 2 - 9 = -7
- The y-coordinate of R' is -4 + 1 = -3

Therefore, the pentagon LMPQR was translated to create L'M'P'Q'R' by moving each vertex to the left by 9 units and up by 1 unit. So the correct answer is "To the left by 9 units and 1 unit up".