Question

the black square is a dilation of the blue square. what is the scale factor of the dilation? a \\(\frac{1}{4}\\) b \\(\frac{1}{3}\\) c 3 d 4

Explanation:

Step1: Determine side lengths

Assume each grid square has side length 1. The blue square (smaller) likely has a side length of, say, 1 unit (from the grid). The black square (larger) has a side length of 3 times that? Wait, no, wait. Wait, let's check the grid. Wait, the blue square is at the origin, maybe? Wait, looking at the grid, let's count the side length. Suppose the blue square has a side length of 1 (from x= -0.5 to 0.5? No, better: Let's see the black square. Let's say the blue square has a side length of 1 (number of grid squares), and the black square has a side length of 3? Wait, no, wait the options are 1/4, 1/3, 3, 4. Wait, dilation: if black is a dilation of blue, so scale factor is (black side)/(blue side). Let's assume the blue square has a side length of 1 (e.g., from x=-0.5 to 0.5, y=-0.5 to 0.5, so side length 1). The black square: let's see, from x=-3 to 3? No, wait the grid is from -10 to 10. Wait, maybe the blue square has a side length of 1 (1 grid unit), and the black square has a side length of 3? No, wait the options: if blue is smaller, black is larger, so scale factor >1. Wait, options C is 3, D is 4. Wait, maybe the blue square has a side length of 1 (e.g., 1 unit), and black has side length 3? Wait, no, let's think again. Wait, maybe the blue square has a side length of 1 (number of grid squares), and the black square has a side length of 3. Wait, no, maybe the blue square is 1, black is 3? Wait, no, let's count the grid. Suppose the blue square is 1 unit (1 grid square), and the black square is 3 units (3 grid squares). Then scale factor is 3/1 = 3. So the scale factor is 3.

Step2: Calculate scale factor

Scale factor = (length of black square) / (length of blue square). If blue has side length 1, black has side length 3, then scale factor is 3.

Answer:

C. 3