Question

Which expression can be used to determine the length of segment ZY?

Answer 1

As we move from point Z to point Y, x increases by 8 and y increases by 3.  Thus the length of line segment ZY is sqrt(8^2 + 3^2) = sqrt(73), by the Pythagorean Theorem.  That's approx. 8.54.

You could also leave your answer in the form √(8^2 + 3^2).

Answer 2

Answer:

Option 2:   $YZ = \sqrt{(3)^{2}+(8)^{2} }$

Step-by-step explanation:

We can see that XYZ is forming right angled triangle in the given figure

where XY is Perpendicular.

XZ is Base.

YZ is Hypotenuse .

Length of XY is 3 units (refer figure)

Length of XZ is 8 units (refer figure)

Now to calculate length of ZY we will use Pythagoras theorem i.e.

$(Hypotenuse)^{2} = (Perpendicular)^{2} +(Base)^{2}$

By applying this theorem :

$(YZ)^{2} = (XY)^{2} +(XZ)^{2}$

$(YZ)^{2} = (3)^{2} +(8)^{2}$

⇒$YZ = \sqrt{(3)^{2}+(8)^{2} }$

Thus Option 2 is the correct expression to determine length of ZY i.e.$YZ = \sqrt{(3)^{2}+(8)^{2} }$