Answer :
Sure, let’s walk through the step-by-step process required to transform the ordered pair (-2, 4) to (-4, 7) and then another transformation to a final point.
### Step 1: Initial Ordered Pair
We start with the ordered pair (-2, 4).
### Step 2: Translation Transformation
To transform this point, apply a translation. A translation shifts a point by adding a vector to it. Here, we can use the translation vector (-2, 3).
- The translation vector is (-2, 3).
Applying this translation to the initial point (-2, 4):
[tex]\[ \text{Translated point} = (-2 + (-2), 4 + 3) = (-4, 7) \][/tex]
### Step 3: Scaling Transformation
Next, we apply a scaling transformation. Scaling adjusts the coordinates by multiplying them by a scalar value. Here, we use a scaling factor of 2.
Applying this scaling to the translated point (-4, 7):
- Scaling factor is 2.
[tex]\[ \text{Scaled point} = (-4 \times 2, 7 \times 2) = (-8, 14) \][/tex]
### Step 4: Identifying the Final Point
The final point after the composite transformation is (-8, 14).
So, the example of a composite transformation that could transform the ordered pair (-2, 4) involves first applying a translation by vector (-2, 3) to get (-4, 7) and then scaling this result by a factor of 2 to get (-8, 14).
### Step 1: Initial Ordered Pair
We start with the ordered pair (-2, 4).
### Step 2: Translation Transformation
To transform this point, apply a translation. A translation shifts a point by adding a vector to it. Here, we can use the translation vector (-2, 3).
- The translation vector is (-2, 3).
Applying this translation to the initial point (-2, 4):
[tex]\[ \text{Translated point} = (-2 + (-2), 4 + 3) = (-4, 7) \][/tex]
### Step 3: Scaling Transformation
Next, we apply a scaling transformation. Scaling adjusts the coordinates by multiplying them by a scalar value. Here, we use a scaling factor of 2.
Applying this scaling to the translated point (-4, 7):
- Scaling factor is 2.
[tex]\[ \text{Scaled point} = (-4 \times 2, 7 \times 2) = (-8, 14) \][/tex]
### Step 4: Identifying the Final Point
The final point after the composite transformation is (-8, 14).
So, the example of a composite transformation that could transform the ordered pair (-2, 4) involves first applying a translation by vector (-2, 3) to get (-4, 7) and then scaling this result by a factor of 2 to get (-8, 14).
