Question

2 what is the length of segment ox?
options: 7.070, 5.000, 1.767, 3.535

Explanation:

Step1: Find midpoint O coordinates

First, calculate the midpoint O of the square (it is also the midpoint of XZ or WY). Using midpoint formula for X(6, -5) and Z(11, -10):
$$O_x = \frac{6+11}{2} = 8.5, \quad O_y = \frac{-5+(-10)}{2} = -7.5$$
So $O(8.5, -7.5)$

Step2: Apply distance formula to OX

Use distance formula between X(6, -5) and O(8.5, -7.5):
$$OX = \sqrt{(8.5-6)^2 + (-7.5-(-5))^2}$$
$$= \sqrt{(2.5)^2 + (-2.5)^2}$$
$$= \sqrt{6.25 + 6.25} = \sqrt{12.5} \approx 3.535$$
Alternatively, note that in a square, diagonals bisect each other, so OX = OZ, and OZ is given as 3.535, so OX equals this value.

Answer:

3.535 (Option: 3.535)