Question

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Explanation:

Step1: Identify the shapes

The figure has two trapezoids (or similar quadrilaterals) and two triangles? Wait, actually, looking at the grid, the red and blue figures are similar trapezoids? Wait, no, maybe they are trapezoids or isosceles trapezoids. Wait, the key is to find the transformation. Wait, maybe it's a dilation or scaling. Let's check the coordinates. Let's assume each grid square is 1 unit. Let's find the top base, middle base, and bottom base.

For the blue (inner) figure: Let's say the top base is length 1 (from x=-0.5 to x=0.5, so length 1), middle part? Wait, no, the blue figure is a trapezoid? Wait, no, the blue figure looks like a smaller trapezoid inside the red larger trapezoid. Let's check the horizontal lengths. The bottom base of red: from x=-3 to x=3? Wait, no, looking at the grid, the red bottom base is from, say, x=-4 to x=4? Wait, maybe the red figure has top base length 2 (from x=-1 to x=1), middle? Wait, no, the red figure's top horizontal segment is length 2 (between the two red vertical segments), and the bottom horizontal segment is length 8? Wait, no, maybe each grid is 1 unit. Let's count the grid squares. The red figure: top base (horizontal) is 2 units (from x=-1 to x=1, so length 2), the bottom base is 8 units? Wait, no, the red bottom base is from x=-4 to x=4, so length 8? Wait, no, the blue bottom base is from x=-2 to x=2, length 4? Wait, no, maybe the scale factor. Let's see the top base of red: 2 units, top base of blue: 1 unit. Bottom base of red: 8 units? No, wait the red bottom base is from x=-4 to x=4? No, the red bottom is from x=-3 to x=3? Wait, maybe the blue figure is a dilation of the red figure with a scale factor of 1/2? Wait, no, let's check the vertical distance. The height of red: from y=0 to y=4? Wait, no, the red figure's height (vertical distance from top to bottom) is, say, 4 units (from y=4 to y=0), and blue's height is 2 units? Wait, no, maybe the scale factor is 1/2. Wait, the key is to find the scale factor between the two figures. Let's take the top horizontal length: red top is 2 units (from x=-1 to x=1), blue top is 1 unit (from x=-0.5 to x=0.5). The bottom horizontal length: red bottom is 6 units (from x=-3 to x=3), blue bottom is 3 units (from x=-1.5 to x=1.5). Wait, no, maybe the scale factor is 1/2? Wait, no, 2 to 1 is 1/2, 6 to 3 is 1/2, and the height: red height is 4 (from y=4 to y=0), blue height is 2 (from y=2 to y=0)? Wait, no, the blue figure is inside, so maybe the scale factor is 1/2. Wait, but maybe the problem is to find the scale factor of dilation from blue to red. Let's check the lengths. Suppose the blue figure has top base length 1, bottom base length 3, and red has top base length 2, bottom base length 6. So scale factor is 2. Wait, 12=2, 32=6. So the scale factor from blue to red is 2.

Step2: Confirm the scale factor

Looking at the horizontal segments: the top horizontal of blue is 1 unit (between the two blue vertical segments), top horizontal of red is 2 units (between the two red vertical segments). The bottom horizontal of blue is 3 units (between the two blue bottom vertical segments), bottom horizontal of red is 6 units. So the scale factor is 2 (since 12=2, 32=6). So the transformation is a dilation with scale factor 2.

Answer:

The scale factor of the dilation (enlargement) from the blue (inner) figure to the red (outer) figure is 2.