To find the length of LM, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point L are (-2, 6) and the coordinates of point M are (-3, 7).
Substituting these values into the distance formula:
d = √((-3 - (-2))^2 + (7 - 6)^2)
Simplifying:
d = √((-3 + 2)^2 + (7 - 6)^2)
d = √((-1)^2 + (1)^2)
d = √(1 + 1)
d = √2
So, the length of LM is approximately √2 to the nearest thousandths.