Question

the diagram shows several planes, lines, and points.
which statement is true about line $h$?
○ line $h$ intersects line $f$ at two points, a and b.
○ line $h$ is the intersection of planes $\mathcal{r}$ and $\mathcal{t}$.
○ line $h$ intersects plane $\mathcal{p}$ at point c.
○ line $h$ has points on planes $\mathcal{r}$, $\mathcal{p}$, and $\mathcal{t}$.

Explanation:

• Analyze each option:

1. Two distinct lines intersect at at most one point, so line $h$ cannot intersect line $f$ at two points (A and B).
2. The intersection of planes $\mathcal{R}$ and $\mathcal{T}$ is not line $h$; plane $\mathcal{T}$ intersects $\mathcal{R}$ at a different line, and plane $\mathcal{P}$ intersects $\mathcal{R}$ at line $h$.
3. Line $h$ lies entirely on plane $\mathcal{R}$ and intersects plane $\mathcal{P}$ at point B, not point C (point C is on plane $\mathcal{P}$ and line $l$, not line $h$).
4. Line $h$ has point B on plane $\mathcal{P}$, point A on plane $\mathcal{T}$, and the entire line lies on plane $\mathcal{R}$, so it has points on all three planes.

Answer:

D. Line $h$ has points on planes $\mathcal{R}$, $\mathcal{P}$, and $\mathcal{T}$.