Final answer:
By computing the distances between points within each set, it is evident that the two sets of points are not congruent as their corresponding side lengths do not match.
Step-by-step explanation:
To determine if the sets of points F(4,6), G(5,7), H(7,4) and J(1,-4), K(2,-5), L(4,-2) are congruent, we need to consider whether there is a transformation that can map one set onto the other exactly.
Congruent figures have the same size and shape, and a congruent transformation can be a combination of translations, rotations, and reflections.
Let's analyze the distances between the points within each set to see if they match:
- FG = √((5-4)^2 + (7-6)^2) = √2
- GH = √((7-5)^2 + (4-7)^2) = √8
- FH = √((7-4)^2 + (4-6)^2) = √9
- JK = √((2-1)^2 + (-5+4)^2) = √2
- KL = √((4-2)^2 + (-2+5)^2) = √10
- JL = √((4-1)^2 + (-2+4)^2) = √10
The distances FG and JK match, suggesting that the sides of the corresponding figures may be congruent. However, the distances GH and KL, FH and JL do not match.
This implies that the sets of points do not form congruent figures. No simple transformation such as translation, rotation, or reflection can make these two sets of points congruent because their corresponding sides are not all equal in length.