△XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1). Which of the following can be used to prove that △XYZ is isosceles?(1 point)
We need to calculate the lengths of XY, YZ, and XZ and see if any two are equal.
Using the distance formula:
- XY = √[(0-2)^2 + (-2-0)^2] = √8
- YZ = √[(-1-0)^2 + (1-(-2))^2] = √10
- XZ = √[(-1-2)^2 + (1-0)^2] = √10
Therefore, XY and YZ are not equal, but both are equal to XZ, so △XYZ is isosceles.
The answer is: XZ = YZ