Question

1. given the diagram, below which statements are true? statement 1: points z, a, and x are collinear. statement 2: points w, a, and y are noncoplanar. statement 3: rays $overrightarrow{wa}$ and $overrightarrow{ay}$ are on the line $overleftrightarrow{wy}$. statement 4: $overrightarrow{aw}$ and $overrightarrow{ay}$ are opposite rays on the line $overleftrightarrow{wy}$. statement 1, 3 and 4 statements 1 and 2 statements 1 and 4 statements 1, 2, 3 and 4

Explanation:

Step1: Check collinearity

Points Z, A, and X do not lie on the same straight - line, so statement 1 is false.

Step2: Check coplanarity

Points W, A, and Y are in the same plane (the plane of the square in the diagram), so statement 2 is false.

Step3: Check ray - line relationship

Rays $\overrightarrow{WA}$ and $\overrightarrow{AY}$ are on the line $\overleftrightarrow{WY}$, so statement 3 is true.

Step4: Check opposite rays

$\overrightarrow{AW}$ and $\overrightarrow{AY}$ are opposite rays on the line $\overleftrightarrow{WY}$ since they have a common endpoint A and extend in opposite directions on the same line, so statement 4 is true.

Answer:

No correct option provided (but statements 3 and 4 are true).