Question

carson claims that a line will always intersect a plane at only one point, and he draws this picture to show his reasoning. iza thinks it is possible for a line to intersect a plane at more than one point. who is correct? explain

Explanation:

To determine who is correct, we analyze the relationship between a line and a plane:

1. Case 1: Line intersects plane at one point

This occurs when the line is not contained within the plane (it "passes through" the plane at a single point, like Carson’s diagram).

1. Case 2: Line lies on the plane

If a line is entirely contained within a plane (i.e., the line "lies in" the plane), then every point on the line is also on the plane. Thus, the line intersects the plane at infinitely many points (all points on the line).

Carson’s claim ("always intersect at one point") is incorrect because he only considers the first case. Iza is correct because a line can lie in a plane (e.g., the x - axis lying in the xy - plane), resulting in infinitely many intersection points.

For the dropdowns:

• First "Select Choice": Iza (she is correct).
• Second "Select Choice": can (a line can lie in a plane).
• Third "Select Choice": infinitely many points (if the line lies in the plane, all its points intersect the plane).

Answer:

First dropdown: Iza
Second dropdown: can
Third dropdown: infinitely many points

(Explanation: A line can either intersect a plane at one point (if it passes through but is not in the plane) or lie in the plane, intersecting it at infinitely many points. Thus, Iza is correct because a line can lie in a plane, resulting in infinitely many intersection points.)