Answer:
The correct option is C.
Step-by-step explanation:
In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.
Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.
The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.
The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.
From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].
It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is
[tex]Z=Z_2(-1,2)[/tex]
Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.
Hence the correct option is C.
