The vertices of ∆GHJ are G(-2,3), and J(1,3). If ∆KLM ≅ ∆GHJ, fing LM.

Well, since the triangles ∆KLM and ∆GHJ are congruent, that means they have the same shape and size. So the corresponding sides of the triangles must be equal in length.

Now, let's find the length of GJ. The coordinates of G are (-2,3) and J is (1,3). So, the distance between G and J can be calculated using the distance formula: √((x2-x1)^2 + (y2-y1)^2).

Using this formula, we get √((1-(-2))^2 + (3-3)^2) = √(3^2 + 0^2) = √9 = 3.

Since ∆KLM ≅ ∆GHJ, the length of LM must also be 3.

So, LM = 3.

But let's not take this answer too lightly, it might actually hold up!

To find LM, we need to find the coordinates of points K and L.

Since ∆KLM is congruent to ∆GHJ, the corresponding sides should have the same lengths.

Given that G(-2, 3) and J(1, 3), we can use these coordinates to find the distance between G and J.

The distance formula is: d = √((x2 - x1)^2 + (y2 - y1)^2)

Using G(-2, 3) and J(1, 3), the distance between G and J is:

d = √((1 - (-2))^2 + (3 - 3)^2)
= √(3^2 + 0^2)
= √(9 + 0)
= √9
= 3

Since ∆KLM is congruent to ∆GHJ, the length of LM should also be 3.

Therefore, LM = 3.

To find LM, we first need to determine the coordinates of point K in triangle ∆KLM.

Since triangles ∆KLM and ∆GHJ are congruent, it means they have the same size and shape. In other words, corresponding sides and corresponding angles are equal.

Given that points G and J are (-2, 3) and (1, 3) respectively, we can assume that the corresponding points in triangle ∆KLM are (-2, 3) and (1, 3) as well.

Now, let's find the coordinates of point L.

Since we know that triangle ∆KLM is congruent to triangle ∆GHJ, we can assume that the corresponding sides GH and KL are also equal in length.

The distance formula can be used to find the lengths of the sides. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the length of side GH:

GH = √((-2 - 1)^2 + (3 - 3)^2)
= √((-3)^2 + 0^2)
= √(9 + 0)
= √9
= 3

Since triangle ∆KLM is congruent to triangle ∆GHJ, the length of side KL should also be 3.

Therefore, LM = KL = 3.