Find the image of the point in the specified plane
(i) (5,4,-3) in the xy plane
(ii) (-2,0,0) in the xy plna e
(iii) (-3,4,7) in the yz plane
(iv) (-7,2,-1) in the zx plane
(iv) (-4,0,1) in the zx plane

Answer

To find the image of a point in a specified plane, we reflect the point across that plane. The reflection process depends on the coordinates of the point and the plane in question.

### Step-by-Step Solution:

**(i) Find the image of the point (5, 4, -3) in the xy-plane:**

1. **Identify the coordinates**: The point is (5, 4, -3).
2. **Understand the reflection**: In the xy-plane, the z-coordinate changes sign while x and y remain the same.
3. **Calculate the image**: The image will be (5, 4, -(-3)) = (5, 4, 3).

**Image in xy-plane**: (5, 4, 3)

---

**(ii) Find the image of the point (-2, 0, 0) in the xy-plane:**

1. **Identify the coordinates**: The point is (-2, 0, 0).
2. **Understand the reflection**: Again, in the xy-plane, the z-coordinate changes sign.
3. **Calculate the image**: The image will be (-2, 0, -0) = (-2, 0, 0).

**Image in xy-plane**: (-2, 0, 0)

---

**(iii) Find the image of the point (-3, 4, 7) in the yz-plane:**

1. **Identify the coordinates**: The point is (-3, 4, 7).
2. **Understand the reflection**: In the yz-plane, the x-coordinate changes sign while y and z remain the same.
3. **Calculate the image**: The image will be (-(-3), 4, 7) = (3, 4, 7).

**Image in yz-plane**: (3, 4, 7)

---

**(iv) Find the image of the point (-7, 2, -1) in the zx-plane:**

1. **Identify the coordinates**: The point is (-7, 2, -1).
2. **Understand the reflection**: In the zx-plane, the y-coordinate changes sign while x and z remain the same.
3. **Calculate the image**: The image will be (-7, -2, -1).

**Image in zx-plane**: (-7, -2, -1)

---

**(v) Find the image of the point (-4, 0, 1) in the zx-plane:**

1. **Identify the coordinates**: The point is (-4, 0, 1).
2. **Understand the reflection**: In the zx-plane, the y-coordinate changes sign.
3. **Calculate the image**: The image will be (-4, -0, 1) = (-4, 0, 1).

**Image in zx-plane**: (-4, 0, 1)

---