Question

Planes X and Y and points C, D, E, and F are shown.

Answer 1

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.

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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.

Answer 2

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.