3. On a $2 \times 3$ rectangular grid paper, the vertices of each small square are called lattice points. Then the number of isosceles right triangles with lattice points as vertices is ( ).
(A) 24
(B) 38
(C) 46
(D) 50
3. D.

The lengths of line segments with grid points as vertices can take 8 values: $1, \sqrt{2}, 2, \sqrt{5}, 2 \sqrt{2}, 3, \sqrt{10}, \sqrt{13}$. The isosceles right triangles formed by these line segments can be classified into 4 cases based on their side lengths:
$$
1,1, \sqrt{2} ; \sqrt{2}, \sqrt{2}, 2 ; 2,2,2 \sqrt{2} ; \sqrt{5}, \sqrt{5}, \sqrt{10} \text {. }
$$

Below, we count the triangles by classifying them according to the length of the hypotenuse.
(1) When the hypotenuse is $\sqrt{2}$, the hypotenuse must be the diagonal of a small square, and there are 12 such line segments. Each such line segment corresponds to two isosceles right triangles, totaling $2 \times 12=24$.
(2) When the hypotenuse is 2, there are 10 line segments of length 2 in the figure, 6 of which are on the perimeter of a $2 \times 3$ rectangle, each corresponding to one isosceles right triangle; the other 4 are inside the $2 \times 3$ rectangle, each corresponding to two isosceles right triangles, totaling $6+2 \times 4=14$.
(3) When the hypotenuse is $2 \sqrt{2}$, the hypotenuse must be the diagonal of a $2 \times 2$ square, and there are 4 such diagonals. Each such line segment corresponds to two isosceles right triangles, totaling $2 \times 4=8$.
(4) When the hypotenuse is $\sqrt{10}$, there are 4 such line segments, each corresponding to one isosceles right triangle, totaling 4.

Therefore, the number of isosceles right triangles with grid points as vertices is $24+14+8+4=50$.