Question

use the following image to determine which of the following statements is true.
i. p is collinear with b and j
ii. j, p and b are all points.
iii. jp is a ray.
iv. pj is a line.
v. p, b and j lie on the same plane.

Explanation:

Step1: Analyze collinearity (Statement I)

Collinear points lie on the same straight line. From the image, \(P\) and \(J\) are on a line, but \(B\) is not on that line. So, \(P\) is not collinear with \(B\) and \(J\).

Step2: Check if they are points (Statement II)

In geometry, \(J\), \(P\), and \(B\) are represented as distinct dots, which are defined as points.

Step3: Define a ray (Statement III)

A ray has one endpoint and extends infinitely in one direction. \(JP\) has endpoint \(J\) and extends through \(P\), so \(JP\) is a ray.

Step4: Define a line (Statement IV)

A line extends infinitely in both directions. \(PJ\) is part of a ray (from \(J\) through \(P\)), not a line.

Step5: Check coplanarity (Statement V)

Since \(P\), \(B\), and \(J\) are all within the given plane (the figure shown is a plane), they lie on the same plane.

Answer:

II. \(J\), \(P\) and \(B\) are all points.; III. \(JP\) is a ray.; V. \(P\), \(B\) and \(J\) lie on the same plane.