Transformations Worksheets, Questions and Revision | MME - Free Printable

Problem Analysis:

The image shows a triangle labeled "A" on a coordinate grid. The task likely involves determining the area of the triangle or performing some geometric transformation (e.g., translation, rotation, reflection). Since no specific task is mentioned in the question, I will assume the primary goal is to calculate the area of the triangle.

Step-by-Step Solution:

#### 1. Identify the Coordinates of the Triangle's Vertices:
From the image, we can read the coordinates of the vertices of the triangle:
- Vertex 1: \( (1, 1) \)
- Vertex 2: \( (4, 1) \)
- Vertex 3: \( (2, 3) \)

#### 2. Use the Formula for the Area of a Triangle Given Its Vertices:
The formula for the area of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is:
\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

Substitute the coordinates of the vertices:
- \((x_1, y_1) = (1, 1)\)
- \((x_2, y_2) = (4, 1)\)
- \((x_3, y_3) = (2, 3)\)

#### 3. Plug the Values into the Formula:
\[
\text{Area} = \frac{1}{2} \left| 1(1 - 3) + 4(3 - 1) + 2(1 - 1) \right|
\]

#### 4. Simplify the Expression Inside the Absolute Value:
\[
\text{Area} = \frac{1}{2} \left| 1(-2) + 4(2) + 2(0) \right|
\]
\[
\text{Area} = \frac{1}{2} \left| -2 + 8 + 0 \right|
\]
\[
\text{Area} = \frac{1}{2} \left| 6 \right|
\]
\[
\text{Area} = \frac{1}{2} \times 6 = 3
\]

#### 5. Final Answer:
The area of the triangle is:
\[
\boxed{3}
\]

Explanation:

- The formula used is a standard method for calculating the area of a triangle when its vertices are known.
- The absolute value ensures that the area is always positive, regardless of the order of the vertices.
- The calculation is straightforward once the coordinates are substituted into the formula.

If the task involves something other than finding the area (e.g., transformations), please provide additional details, and I can adjust the solution accordingly.