Fill in the blanks :
`{:("Point","Transformation ","Image"),((5, -7), .....................,(-5, 7)):}`

Answer

To solve the problem, we need to fill in the blanks in the statement regarding the transformation of the point (5, -7) and its image (-5, 7). Here’s the step-by-step solution:

### Step 1: Identify the Points
We have two points:
- Point P: (5, -7)
- Point Q: (-5, 7)

### Step 2: Understand the Transformation
The transformation we are looking at is a reflection. The question implies that point Q is the reflection of point P with respect to the origin.

### Step 3: Calculate the Distance from the Origin
To confirm that these points are reflections of each other, we can calculate their distances from the origin (0, 0).

**Distance of Point P from Origin:**
Using the distance formula:
\[ OP = \sqrt{x^2 + y^2} = \sqrt{5^2 + (-7)^2} = \sqrt{25 + 49} = \sqrt{74} \]

**Distance of Point Q from Origin:**
Using the distance formula:
\[ OQ = \sqrt{x^2 + y^2} = \sqrt{(-5)^2 + 7^2} = \sqrt{25 + 49} = \sqrt{74} \]

### Step 4: Conclusion about Reflection
Since both distances are equal (both are \(\sqrt{74}\)), we conclude that point Q is indeed the reflection of point P with respect to the origin.

### Step 5: Fill in the Blanks
Now we can fill in the blanks in the statement:
- The transformation is a reflection in the origin.

Thus, the complete statement is:
`{:("Point","Transformation ","Image"),((5, -7), "Reflection in Origin", (-5, 7))}`

### Final Answer
- Point: (5, -7)
- Transformation: Reflection in Origin
- Image: (-5, 7)

---