Respuesta :
Answer: The correct option is
(B) The line that can be drawn through points D and E is contained in plane Y.
Step-by-step explanation: The planes X and Y and points C, D, E and F are shown in the given figure.
We are to select the TRUE statement about the points and the planes.
We know that, if two points lie in a plane, then the line drawn through the points will contained in the same plane.
The points C lies outside the plane Y and the point D lies on the plane Y, so the line drawn through the points C and D will not contained in plane Y.
So, option (A) is NOT correct.
The points D and E, both lie in the plane Y, so the line drawn through the points D and E will also contained in plane Y.
So, option (B) is CORRECT.
Since the plane X contain infinitely many points, so F is not the only point that can lie in plane X.
So, option (C) is NOT correct.
Similarly, there are infinitely many points in the plane Y, so the points D and E are not the only points that can lie in plane Y.
So, option (D) is NOT correct.
Thus, the correct option is
The line that can be drawn through points D and E is contained in plane Y.
Option (B) is CORRECT.
The line that can be drawn through points D and E is contained in plane Y. Option (b) is correct.
Further Explanation:
Given:
The options are as follows,
(a). The line that can be drawn through points C and D is contained in plane Y.
(b). The line that can be drawn through points D and E is contained in plane Y.
(c). The only point that can lie in plane X is point F.
(d). The only points that can lie in plane Y are points D and E.
Explanation:
In option (a)
The point D lies on plane Y and point C lies outside the plane Y. Therefore, the line from C to D doesn’t contain plane Y.
Option (a) is not correct.
In option (b)
The point D lies on plane Y and point E lies on the plane Y. Therefore, the line from E to D does contain plane Y.
Option (b) is correct.
In option (c)
Plane X can contain infinitely many solutions and F is not the only point on plane X.
Option (c) is not correct.
In option (d)
Plane Y can contain infinitely many solutions and D and E are not the only point on plane Y.
Option (d) is not correct.
The line that can be drawn through points D and E is contained in plane Y. Option (b) is correct.
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Three dimensions
Keywords: planes, plane X, plane Y, points, statements, true, the line, drawn, point C, lie, point D.
