Question

notes
kuta software - infinite pre-algebra
translations of shapes
graph the image of the figure using the transformation given.

1. translation: 1 unit left
2. translation: 1 unit right and 2 units down

Explanation:

1) Translation: 1 unit left

Step1: Identify original vertices

Let's assume the original figure (lower left) has vertices. For example, if we take the key points (let's say the base vertices and the peak). Suppose original coordinates (we can infer from grid, but since it's a translation, the process is: for each vertex \((x,y)\), new coordinate is \((x - 1,y)\) (since left translation subtracts 1 from x - coordinate).

Step2: Apply translation

Take each vertex of the original shape, subtract 1 from the x - coordinate (keep y - coordinate same) and plot the new points, then connect them. For example, if a vertex is at \((2,3)\), after translation it becomes \((1,3)\). Repeat for all vertices and draw the image.

2) Translation: 1 unit right and 2 units down

Step1: Identify original vertices (triangle with vertices, say, E, T, I)

Find the coordinates of each vertex of the original triangle (from the grid). Let's assume E is at \((x_E,y_E)\), T at \((x_T,y_T)\), I at \((x_I,y_I)\).

Step2: Apply translation rule

For a translation 1 unit right (add 1 to x - coordinate) and 2 units down (subtract 2 from y - coordinate), the new coordinates are \((x + 1,y - 2)\) for each vertex. For example, if E is at \((-1,2)\), new E is \((-1 + 1,2 - 2)=(0,0)\); if T is at \((-1,4)\), new T is \((-1+1,4 - 2)=(0,2)\); if I is at \((-3,4)\), new I is \((-3 + 1,4 - 2)=(-2,2)\). Then plot these new points and connect them to get the translated triangle.

Answer:

1. The translated figure (1 unit left) is obtained by shifting each vertex of the original figure 1 unit to the left (subtracting 1 from x - coordinates, keeping y - coordinates same) and redrawing the shape.
2. The translated figure (1 unit right, 2 units down) is obtained by shifting each vertex of the original triangle 1 unit right (adding 1 to x - coordinates) and 2 units down (subtracting 2 from y - coordinates) and redrawing the triangle.

(Note: Since it's a graphing problem, the final answer is the visual representation after applying the translation rules as described. The key is to apply the \((x\pm a,y\pm b)\) translation rules where \(a = 1,b = 0\) for left translation and \(a = 1,b=- 2\) for right - down translation.)