Question Video: Understanding the Relation between a Plane and a Straight Line | Nagwa Question Video: Understanding the Relation between a Plane and a Straight Line | Nagwa

# Question Video: Understanding the Relation between a Plane and a Straight Line Mathematics • Second Year of Secondary School

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Observe the given figure and choose the correct statement. [A] The straight line is parallel to the plane. [B] The straight line is contained within the plane. [C] The straight line intersects the plane.

02:15

### Video Transcript

Observe the given figure and choose the correct statement. Option (A) the straight line is parallel to the plane. Option (B) the straight line is contained within the plane. Or option (C) the straight line intersects the plane.

In the figure, we can observe that we have a plane, defined as 𝑋, that extends infinitely in all directions. We can also see that there is a point 𝐴, which lies on the plane. The point 𝐴 also lies on the line 𝐿. And then because the plane 𝑋 and the line 𝐿 share this common point 𝐴, then we can say that the straight line 𝐿 intersects the plane. Therefore, the correct statement is that given in option (C). The straight line intersects the plane.

But before we finish this question, it might be worth considering what the other two answer options might look like on a diagram. In option (A), if we wanted to illustrate a line which is parallel to a plane, then it might look something a little bit like this. But we should recall that a line and plane which are parallel will never intersect. And in this diagram, we know that the line and the plane intersect at a point 𝐴. So, option (A) is incorrect.

For option (B), if we were to create a line which is contained within a plane, it might look something like this. When a line is contained within a plane, that means that every point on the line also lies on the plane. It is at this point that the way in which the diagram is drawn is particularly important. It is the dashed or dotted part of the line 𝐿 from this intersection point 𝐴 which indicates that not all of this line is contained in the plane. And so statement (B) would be incorrect. Therefore, the correct statement is that the straight line intersects the plane.

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