Question

mini project: create a design or shape that has at least 10 different end points, then translate the image both horizontally and vertically. write down the coordinates before and after the translation.
notation: (x, y) → _______________

Explanation:

Step1: Design a Shape (Rectangle)

Let's create a rectangle with vertices at \((2, 2)\), \((8, 2)\), \((8, 6)\), \((2, 6)\) and also add some more points to reach at least 10 endpoints. Let's take a more complex shape, say a polygon with vertices: \((1, 1)\), \((1, 5)\), \((5, 5)\), \((5, 1)\), \((3, 3)\), \((3, 7)\), \((7, 7)\), \((7, 3)\), \((2, 2)\), \((8, 2)\) (total 10 points).

Step2: Define Translation

Let's translate the shape 3 units right (horizontal) and 2 units up (vertical). The translation rule is \((x, y) \to (x + 3, y + 2)\).

Step3: Calculate New Coordinates

• For \((1, 1)\): \(x = 1 + 3 = 4\), \(y = 1 + 2 = 3\) → \((4, 3)\)
• For \((1, 5)\): \(x = 1 + 3 = 4\), \(y = 5 + 2 = 7\) → \((4, 7)\)
• For \((5, 5)\): \(x = 5 + 3 = 8\), \(y = 5 + 2 = 7\) → \((8, 7)\)
• For \((5, 1)\): \(x = 5 + 3 = 8\), \(y = 1 + 2 = 3\) → \((8, 3)\)
• For \((3, 3)\): \(x = 3 + 3 = 6\), \(y = 3 + 2 = 5\) → \((6, 5)\)
• For \((3, 7)\): \(x = 3 + 3 = 6\), \(y = 7 + 2 = 9\) → \((6, 9)\)
• For \((7, 7)\): \(x = 7 + 3 = 10\), \(y = 7 + 2 = 9\) → \((10, 9)\)
• For \((7, 3)\): \(x = 7 + 3 = 10\), \(y = 3 + 2 = 5\) → \((10, 5)\)
• For \((2, 2)\): \(x = 2 + 3 = 5\), \(y = 2 + 2 = 4\) → \((5, 4)\)
• For \((8, 2)\): \(x = 8 + 3 = 11\), \(y = 2 + 2 = 4\) → \((11, 4)\)

Answer:

Before Translation (10 Points):

\((1, 1)\), \((1, 5)\), \((5, 5)\), \((5, 1)\), \((3, 3)\), \((3, 7)\), \((7, 7)\), \((7, 3)\), \((2, 2)\), \((8, 2)\)

After Translation (10 Points, Rule: \((x, y) \to (x + 3, y + 2)\)):

\((4, 3)\), \((4, 7)\), \((8, 7)\), \((8, 3)\), \((6, 5)\), \((6, 9)\), \((10, 9)\), \((10, 5)\), \((5, 4)\), \((11, 4)\)

(Note: The design and translation can be adjusted as per preference, this is one example to meet the 10 endpoints and translation requirements.)