Question

if the rectangle shown at right was translated to form a rectangle with the vertices (-2, 3), (0, 3), (-2, -2), and (0, -2), describe the translation

Explanation:

Step1: Identify original vertices

From the graph, let's assume original vertices (e.g., K, L, J, M). Let's take a point, say K: looking at the grid, if we estimate, original K might be at (-6, 7) (assuming grid lines, each square is 1 unit). Wait, no, let's check the translated vertices: (-2, 3), (0, 3), (-2, -2), (0, -2). Let's find original vertices. Let's take a vertex of the original rectangle. Let's say original vertex J: from the graph, J is at (-6, 2)? Wait, no, the original rectangle is at x between -6 and -4, y between 2 and 7? Wait, no, let's look at the translated vertices: x from -2 to 0, y from -2 to 3. Let's find the translation vector. Let's take a corresponding vertex. Let's say original vertex (let's pick a point from original rectangle: suppose original M is at (-4, 2), and translated M is at (0, -2)? Wait, no, translated vertices are (-2,3), (0,3), (-2,-2), (0,-2). Let's find the original vertices. Let's assume original rectangle has vertices, say, (-6, 7), (-4, 7), (-6, 2), (-4, 2) (looking at the graph: K is at (-6,7), L at (-4,7), J at (-6,2), M at (-4,2)). Now translated vertices: (-2,3), (0,3), (-2,-2), (0,-2).

Step2: Calculate horizontal translation

For x-coordinate: original x (e.g., -6) to translated x (-2). The change is $-2 - (-6) = 4$. So horizontal translation: 4 units to the right (since positive).

Step3: Calculate vertical translation

For y-coordinate: original y (e.g., 7) to translated y (3). The change is $3 - 7 = -4$. So vertical translation: 4 units down (since negative).

Answer:

The rectangle was translated 4 units to the right and 4 units down.