Question

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 WA and AY are on the line WY.
statement 4: AW and AY are opposite rays on the line WY.

1. statement 1, 3 and 4
2. statements 1 and 2
3. statements 1 and 4
4. statements 1, 2, 3 and 4

Answer 1

In the given diagram, the statements that are true are statements 1, 3 and 4. The correct option is the first one - 1. statement 1, 3 and 4

To determine which statements are true, we will consider the statements one after the other

• For statement 1: Points Z, A, and X are collinear.

Collinear points are the set of three or more points that exist on the same straight line.

In the diagram, points Z, A, and X exist on the same straight line, therefore, they are collinear.

Statement 1 is true

• For statement 2: Points W, A, and Y are noncoplanar

Noncoplanar points are a group of points that don't all lie in the same plane.

In the diagram, points W, A, and Y all lie in the same plane, therefore, they are coplanar and not noncoplanar.

Statement 2 is false

• For statement 3:  Rays WA and AY are on the line WY

A ray is a portion of a line which has one endpoint and extends forever in one direction.

In the diagram, rays WA and AY are on the line WY

Statement 3 is true

• For statement 4: AW and AY are opposite rays on the line WY

A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions.

In the diagram, rays AW and AY have the same endpoint and extend in opposite directions, and they also lie on line WY.

Statement 4 is true

Hence, in the given diagram, the statements that are true are statements 1, 3 and 4.

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