Question

In a right triangle, the hypotenuse has endpoints XY, shown on the graph.

below...

If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
A)3
B)4
C)5
D)6

Answer 1

The point z is (-1,2). Then if you count line YZ. There are 5 spaces.

Answer 2

The correct option is C.

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
`Z_1` and
`Z_2`.

It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is

`Z=Z_2(-1,2)`

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.