Question

plane x contains point c. plane y contains points a and b. how many planes exist that pass through points a, b, and c? ○ 0 ○ 1 ○ 2 ○ 3

Explanation:

Step1: Recall the postulate about planes and points

The postulate states that through any three non - collinear points, there is exactly one plane. Also, if three points are collinear, there are infinitely many planes, but in this case, we analyze the positions of points A, B, and C. Plane Y contains A and B, Plane X contains C. We need to see how many planes pass through A, B, C.

Step2: Analyze the collinearity/non - collinearity

Points A and B are in plane Y, point C is in plane X. The three points A, B, C are not collinear (since A and B are in one plane, C in another intersecting plane). By the postulate, there is exactly one plane that can pass through three non - collinear points.

Answer:

1 (corresponding to the option "1")