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.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: