The point P(5,1) and Q(-2,-2) are reflected in line x = 2 . Use graph paper to find the images P' and Q' of points P and Q respectively in line x = 2 . Take 2 cm equal to 2 units.

Answer

To find the images P' and Q' of points P(5,1) and Q(-2,-2) respectively when reflected in the line x = 2, we can follow these steps:

### Step 1: Understand the Reflection Line
The line of reflection is x = 2. This means that any point reflected across this line will have the same y-coordinate, but the x-coordinate will be adjusted based on its distance from the line x = 2.

### Step 2: Determine the Coordinates of Point P
The coordinates of point P are given as (5, 1).

### Step 3: Calculate the Distance from P to the Line x = 2
To find the distance from point P(5, 1) to the line x = 2:
- The x-coordinate of P is 5.
- The distance to the line x = 2 is:
\[ \text{Distance} = 5 - 2 = 3 \]

### Step 4: Find the Image P'
Since the distance from P to the line is 3 units, the image P' will be 3 units on the opposite side of the line x = 2. Therefore:
- The x-coordinate of P' will be:
\[ 2 - 3 = -1 \]
- The y-coordinate remains the same as that of P, which is 1.

Thus, the coordinates of P' are (-1, 1).

### Step 5: Determine the Coordinates of Point Q
The coordinates of point Q are given as (-2, -2).

### Step 6: Calculate the Distance from Q to the Line x = 2
To find the distance from point Q(-2, -2) to the line x = 2:
- The x-coordinate of Q is -2.
- The distance to the line x = 2 is:
\[ 2 - (-2) = 4 \]

### Step 7: Find the Image Q'
Since the distance from Q to the line is 4 units, the image Q' will be 4 units on the opposite side of the line x = 2. Therefore:
- The x-coordinate of Q' will be:
\[ 2 + 4 = 6 \]
- The y-coordinate remains the same as that of Q, which is -2.

Thus, the coordinates of Q' are (6, -2).

### Step 8: Summary of Results
- The image of point P is P'(-1, 1).
- The image of point Q is Q'(6, -2).

### Final Coordinates
- P' = (-1, 1)
- Q' = (6, -2)