Question

1. what are the coordinates of point a?

options: (2, 0, 5), (5, 0, 2), (5, 2, 0), (0, 2, 5)

Explanation:

Step1: Analyze the z - coordinate

Point A is on the same horizontal plane (parallel to the xy - plane) as point E which has coordinates \((0,0,5)\). In a 3 - D coordinate system \((x,y,z)\), the z - coordinate of a point on the same horizontal plane as another point will be the same. So, the z - coordinate of point A is 5.

Step2: Analyze the y - coordinate

Point A is on the same vertical plane (parallel to the xz - plane) as point E (which has \(y = 0\))? Wait, no. Wait, looking at the cube, point A and point E: Wait, let's look at the y - axis. The point \((0,6,0)\) and \((0,6,5)\) have \(y = 6\). Wait, point A: Let's see the y - coordinate. The distance from the y - axis? Wait, no. Wait, the point E is \((0,0,5)\) and point F is \((0,6,5)\). So the side along the y - axis from E to F is length 6. Now, point A: Let's see the y - coordinate. Wait, maybe another way. Let's look at the x, y, z coordinates. The z - coordinate is 5 (from E). Now, the y - coordinate: Let's see the options. The last option is \((0,2,5)\)? Wait, no. Wait, let's check the x, y, z. Wait, the origin is \((0,0,0)\). Let's look at the x - axis: the point D is on the x - axis. Wait, maybe the y - coordinate: Let's see the point A. If we look at the y - axis, the point \((0,6,0)\) is on the y - axis at \(y = 6\). The point A: let's see the y - coordinate. Wait, the correct option: Let's check the z - coordinate first. All points on the same horizontal level as E (z = 5) will have z = 5. So we can eliminate options with z not equal to 5. So \((5,0,2)\) (z = 2), \((5,2,0)\) (z = 0) are out. Now we have \((2,0,5)\), \((0,2,5)\). Now, look at the y - coordinate. Point E is \((0,0,5)\), point A is connected to E? Wait, no. Wait, the cube: E is \((0,0,5)\), A is a vertex. Wait, maybe the y - coordinate: Let's see the point \((0,6,0)\) is on the y - axis. The distance from y = 0 to y = 6 is 6 units. Now, the point A: let's see the y - coordinate. Wait, the correct answer is \((0,2,5)\)? No, wait. Wait, let's re - examine. Wait, the x - coordinate: if the x - axis is as shown, but maybe the x - coordinate of A is 0? Wait, no. Wait, maybe I made a mistake. Wait, the options: \((0,2,5)\): x = 0, y = 2, z = 5. Let's check the z - coordinate: 5 (correct, same as E). y - coordinate: 2? Wait, maybe. Wait, the point E is \((0,0,5)\), and point A is at (0,2,5)? Wait, no, let's check the figure again. Wait, the point A is connected to E and to another point. Wait, maybe the x - coordinate is 0? Wait, the correct answer is \((0,2,5)\)? Wait, no, let's check the options again. Wait, the last option is \((0,2,5)\). Let's verify: z = 5 (correct, same as E), y = 2, x = 0. Yes, that makes sense. Wait, but let's check the x - coordinate. If x = 0, then it's on the y - z plane. So the coordinates of A are \((0,2,5)\).

Answer:

\((0,2,5)\)