Question

name the plane that is highlighted in the diagram below.

Explanation:

Step1: Recall how to name a plane

A plane can be named by three non - collinear points that lie on the plane. Looking at the diagram, the highlighted plane contains points Q, U, W, R (or other combinations of non - collinear points on the plane). One common way is to use three non - collinear points. For example, points Q, U, and W are on the plane, or Q, R, W, but the standard way is to use three non - collinear points. Let's identify the points: Q, U, W, R, etc. The plane can be named using three non - collinear points, say Q, U, W or Q, R, W or U, V, W etc. But looking at the diagram, the plane passes through Q, U, W, R. A common way is to name it using three non - collinear points, for example, Plane QURW (but more accurately, using three non - collinear points like Q, U, W or Q, R, W or U, V, W, or Q, U, R). Wait, actually, in the rectangular prism, the highlighted plane has points Q, U, W, R. So we can name the plane using three non - collinear points on it. Let's take Q, U, and W. Or Q, R, and W. Or U, V, and W. But the correct way is to use three non - collinear points. Let's check the vertices: Q, U, V, W, R, S, T, X. The highlighted plane: let's see the edges. Q is connected to U and R, U is connected to X and V, W is connected to X and S and V, R is connected to S and Q. So the plane contains Q, U, V, W, R, S? Wait, no, the highlighted plane is the one with the blue lines and the shaded area. Looking at the points: Q, U, W, R are on the plane. So we can name the plane as Plane QURW, but in geometry, a plane is named by three non - collinear points. So let's pick three non - collinear points on the plane. For example, Q, U, and W. Or Q, R, and W. Or U, V, and W. Wait, another way: in a rectangular prism, the plane can be named by four points, but the standard is three non - collinear. Let's see the coordinates (mentally): Q, U, V, W, R, S, T, X. The plane in question: let's see the edges. Q to U, U to V, V to W, W to S, S to R, R to Q? No, maybe Q, U, W, R. So the plane can be named as Plane QURW, but more precisely, using three non - collinear points. Let's take Q, U, and W. So the plane is Plane QUW, or Plane QUR, or Plane QWS, etc. Wait, maybe the correct name is Plane QURW, but in geometry, a plane is named by three non - collinear points. Let's check the points: Q, U, R are non - collinear? Q to U is vertical, U to V is horizontal, V to W is horizontal, W to S is vertical, S to R is horizontal, R to Q is horizontal. Wait, Q, U, R: Q is at the bottom front left, U is at the top front left, R is at the bottom front right. So Q, U, R are non - collinear (they form a right triangle). So Plane QUR. Or Q, U, W: Q (bottom front left), U (top front left), W (top back right). These three are non - collinear. So Plane QUW. Alternatively, looking at the diagram, the highlighted plane has points Q, U, V, W, R, S? No, the shaded area: let's see the blue lines. There are lines QU, QW, RS, UW? Wait, maybe the plane is Plane QURW (or Plane QUSW? No, S is at the bottom back right). Wait, maybe the correct name is Plane QURW, but the standard way is to use three non - collinear points. Let's confirm: in geometry, a plane is named by three non - collinear points, or by a capital letter, or by four points (if it's a quadrilateral). So from the diagram, the plane contains points Q, U, V, W, R, S? No, the rectangular prism has 8 vertices: Q, R, S, T (bottom face: Q - R - S - T), U, V, W, X (top face: U - V - W - X), with Q connected to U, R connected to V, S connected to W, T connected to X (vertical edges). The highlighted plane: looking at the shaded area, it includes Q, U, W, R. So the plane can be named as Plane QURW (since Q, U, R, W are on the plane, and they form a quadrilateral, so we can name the plane using these four points, or three of them). So the plane is Plane QURW (or Plane QUW, Plane QWR, Plane QUR, etc.). But the most appropriate name would be using three non - collinear points. Let's take Q, U, and W: Plane QUW. Or Q, R, and W: Plane QRW. Or U, V, and W: Plane UVW. Wait, maybe the correct answer is Plane QURW, but let's check the vertices again. Q (bottom front left), U (top front left), V (top front right), W (top back right), R (bottom front right), S (bottom back right), T (bottom back left), X (top back left). The highlighted plane: the shaded area seems to cover Q, U, V, W, R, S? No, the blue lines are QU, QW, RS, UW? Wait, maybe the plane is Plane QUSW? No, S is bottom back right. Wait, perhaps the plane is Plane QURW. So the name of the plane is Plane QURW (or any three non - collinear points on it, like Plane QUW).

Answer:

Plane QUW (or Plane QURW, Plane QRW, etc. depending on the three non - collinear points chosen; a common correct answer could be Plane QUW or Plane QURW)