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.
select choice v is because a line select choice v lie in a plane and intersect it in select choice v

Explanation:

Step1: Recall Line-Plane Intersection

A line can either intersect a plane at one point, lie entirely in the plane (intersecting at infinitely many points), or be parallel (no intersection).

Step2: Analyze Carson's Claim

Carson says a line always intersects a plane at one point. But a line can lie in the plane (e.g., the line is part of the plane's surface), so his claim is wrong.

Step3: Analyze Iza's Claim

Iza thinks a line can intersect a plane at more than one point. This is true because if a line lies in the plane, every point on the line is an intersection point (infinitely many, which is more than one).

Step4: Evaluate the Diagram

The diagram shows a line passing through a plane at one point, but this is just one case. The key is the geometric principle: a line can lie in a plane (so intersect at infinitely many points) or intersect at one, or be parallel. So Iza is correct because a line can lie in a plane (intersecting at all its points, more than one) or intersect at one. Carson is wrong as he ignores the "line in plane" case.

Answer:

Iza is correct. A line can lie in a plane (intersecting the plane at infinitely many points, which is more than one) or intersect at one point, or be parallel (no intersection). Carson is wrong because he claims a line always intersects at one point, but a line can lie entirely in a plane (e.g., the line is part of the plane’s surface), resulting in infinitely many intersection points.