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



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

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 and .

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

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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x