The OCR of the image is: --- ЗАДАНИЕ №3 Переместите красные точки так, чтобы для получившегося четырехугольника прямая 1 стала осью симметрии. 10 см С Вид по умолчанию Длина стороны одной клетки равна 2 см и известна длина одной из сторон. Найдите периметр получившего четырехугольника: P= 33 см. Ответить --- The image contains a geometry problem. The user is asked to move red dots to make the line 'l' an axis of symmetry for the resulting quadrilateral. The problem states that the length of one grid cell is 2 cm and the length of one side is known. The task is to find the perimeter of the resulting quadrilateral. The image displays a grid with a quadrilateral drawn on it. A dashed red line labeled 'l' is shown, intended to be the axis of symmetry. There are two red dots representing vertices of the quadrilateral. A label '10 cm' is present, indicating the length of one of the sides or a segment. Below the figure, text specifies that the length of one grid cell is 2 cm and that one side's length is known. The question asks to find the perimeter of the quadrilateral. A field shows P = 33 cm, implying a solution has been entered or is being displayed. To solve this problem, we need to understand the properties of symmetry. If line 'l' is the axis of symmetry, then for every point on one side of the line, there is a corresponding point on the other side such that the line segment connecting them is perpendicular to the axis of symmetry and is bisected by it. This means the quadrilateral would be a kite or a rhombus if the axis passes through opposite vertices, or an isosceles trapezoid if the axis is parallel to the bases and passes through the midpoints of the non-parallel sides. However, the instruction explicitly asks to 'Move the red dots so that the line l becomes the axis of symmetry for the resulting quadrilateral.' This implies we need to determine the coordinates of the vertices based on the grid and the symmetry property, and then calculate the perimeter. The provided perimeter '33 cm' might be the correct answer or a value to be verified. Let's assume the dashed line 'l' is indeed the axis of symmetry. The red dots are vertices. Let's denote the vertices of the quadrilateral. We need to count the grid cells to determine lengths and positions. The label '10 cm' likely refers to the length of the slanted side that is not along the grid lines. Since one grid cell is 2 cm, a length of 10 cm corresponds to 5 grid units (10 cm / 2 cm/cell = 5 cells). Let's analyze the given figure assuming 'l' is the axis of symmetry. The line 'l' appears to be a vertical line passing through the middle of the grid. Let's count the grid units from the line 'l' to the red dots. The top red dot is approximately 3 units to the right of 'l'. The bottom red dot is approximately 3 units to the right of 'l'. This implies that the quadrilateral is symmetric with respect to the line 'l'. The shape appears to be a kite or a dart if the axis of symmetry passes through two opposite vertices. However, the red dots are positioned such that they are reflections of each other across the line 'l' if the line 'l' is considered the axis of symmetry. In this case, the line 'l' would be the axis of symmetry of the quadrilateral. Let's consider the lengths of the sides. The horizontal segments appear to be 4 cells long each. So, their lengths are 4 * 2 cm = 8 cm. The slanted sides are indicated by the red dots. The label '10 cm' is next to the left slanted side. If 'l' is the axis of symmetry, then the left slanted side and the right slanted side must have equal lengths. Thus, both slanted sides are 10 cm long. Therefore, the perimeter would be the sum of the lengths of all four sides. Two sides are horizontal, each 8 cm. Two sides are slanted, each 10 cm. Perimeter = 8 cm + 8 cm + 10 cm + 10 cm = 36 cm. However, the image shows P = 33 cm. This suggests my interpretation of the '10 cm' label or the grid dimensions might be incorrect, or the provided '33 cm' is the intended answer derived from a different configuration or a slight inaccuracy in the drawing. Let's re-examine the problem statement and the visual cues. The instruction is to 'Move the red dots so that the line l becomes the axis of symmetry'. This means the initial configuration might not be symmetric, and we need to adjust the positions of the red dots. The question asks for the perimeter of the *resulting* quadrilateral. The input P = 33 cm is given, which could be a target value or a pre-filled answer. Let's assume the '10 cm' refers to one of the slanted sides. If 'l' is the axis of symmetry, then the quadrilateral must be symmetric with respect to 'l'. The figure shows a dashed vertical line 'l'. The two red dots are on the right side of 'l'. For 'l' to be an axis of symmetry, the vertices on the right side must have corresponding vertices on the left side, which are mirror images. If the red dots are the only movable points, then the quadrilateral would be formed by connecting these two red dots to the endpoints of the horizontal segments. Let's assume the horizontal segments are indeed 8 cm each (4 cells * 2 cm/cell). If the perimeter is 33 cm, and two sides are 8 cm each, their total is 16 cm. The remaining perimeter for the two slanted sides is 33 cm - 16 cm = 17 cm. This means each slanted side would be 17 cm / 2 = 8.5 cm. This contradicts the '10 cm' label. Let's reconsider the '10 cm' label. It is placed near the left slanted side. If 'l' is the axis of symmetry, then the right slanted side must also be 10 cm. This would make the total length of the slanted sides 20 cm. If the perimeter is 33 cm, then the two horizontal sides together must be 33 cm - 20 cm = 13 cm. This means each horizontal side would be 13 cm / 2 = 6.5 cm. However, the horizontal sides appear to span 4 cells, which would be 8 cm. This also leads to a contradiction. There seems to be a discrepancy. Let's assume the '33 cm' is the correct perimeter and try to work backward or find a configuration that yields this perimeter, given 'l' is the axis of symmetry. The problem states 'the length of one grid cell is 2 cm'. Let's assume the drawing is a representation, and the key information is: 'l' is the axis of symmetry, cell size is 2 cm, and the perimeter is 33 cm. This implies that the problem might be asking us to find the lengths of the sides such that they sum to 33 cm and the figure is symmetric about 'l'. If 'l' is a vertical axis of symmetry, the quadrilateral must be an isosceles trapezoid or a kite (if 'l' passes through two vertices). Given the drawing, it looks like an isosceles trapezoid where the non-parallel sides are equal. Let the lengths of the parallel sides be $$b_1$$ and $$b_2$$, and the length of the non-parallel sides be $$s$$. The perimeter $$P = b_1 + b_2 + 2s$$. We are given $$P = 33$$ cm. In the drawing, the horizontal segments appear to be the parallel sides. Let's say the top horizontal segment is $$b_1$$ and the bottom horizontal segment is $$b_2$$. The slanted sides are $$s$$. The label '10 cm' is next to a slanted side. If this label is correct, then $$s = 10$$ cm. So, $$2s = 20$$ cm. Then $$b_1 + b_2 = P - 2s = 33 - 20 = 13$$ cm. This means the sum of the lengths of the two horizontal segments is 13 cm. If they are equal, each is 6.5 cm. However, visually, the horizontal segments span 4 cells, which would be $$4 \times 2 = 8$$ cm each. So, $$b_1 = 8$$ cm and $$b_2 = 8$$ cm, and $$b_1 + b_2 = 16$$ cm. This is a contradiction with $$13$$ cm. Let's assume the '10 cm' is not the length of the slanted side, but perhaps the length of one of the horizontal sides, or relates to the grid in a different way. However, the placement strongly suggests it's a side length. Let's consider the possibility that the provided value 'P = 33 cm' is the correct perimeter and we need to deduce the side lengths consistent with symmetry. If 'l' is the axis of symmetry, and the figure is an isosceles trapezoid, the non-parallel sides are equal. Let's assume the horizontal sides are parallel. From the grid, the bottom horizontal side spans 4 cells (8 cm). The top horizontal side also seems to span 4 cells (8 cm). If this is an isosceles trapezoid with parallel horizontal sides of 8 cm each, and the perimeter is 33 cm, then the sum of the two slanted sides is $$33 - 8 - 8 = 17$$ cm. Thus, each slanted side would be $$17 / 2 = 8.5$$ cm. This contradicts the '10 cm' label. However, if the red dots are to be moved, the lengths of the sides can change. Let's assume the label '10 cm' is indeed the length of the slanted side. So, $$s = 10$$ cm. Then the two slanted sides are 20 cm. If the perimeter is 33 cm, the sum of the two horizontal sides is $$33 - 20 = 13$$ cm. Let's assume the horizontal sides are equal, so each is 6.5 cm. On the grid, a length of 6.5 cm corresponds to $$6.5 / 2 = 3.25$$ cells. This is not an integer number of cells. This suggests that either the drawing is not perfectly to scale, or the '10 cm' refers to something else, or the perimeter is not 33 cm, or the '2 cm' per cell is not exact, or the 'l' is not perfectly vertical, or the symmetry is not perfect in the drawing. Given the context of the problem (likely an interactive geometry problem where the user moves points), the most plausible scenario is that the '10 cm' label indicates the length of the slanted side, and the perimeter is indeed 33 cm. The visual representation on the grid might be approximate. If the perimeter is 33 cm and the two slanted sides are 10 cm each, then the sum of the two horizontal sides is $$33 - 10 - 10 = 13$$ cm. If these horizontal sides are equal (due to symmetry), each would be $$13 / 2 = 6.5$$ cm. The cell size is 2 cm, so 6.5 cm is $$3.25$$ cells. This is unusual for a grid-based problem, unless the red dots can be positioned at fractional cell points. Let's consider another interpretation. What if 'l' is the axis of symmetry, and the red dots are symmetric. If 'l' is the axis of symmetry, and we have horizontal segments, this would form an isosceles trapezoid. Let the horizontal bases be $$b_1$$ and $$b_2$$, and the non-parallel sides be $$s$$. The perimeter is $$P = b_1 + b_2 + 2s$$. We are given P=33 cm. Let's assume the '10 cm' refers to one of the slanted sides, so $$s=10$$ cm. Then $$b_1+b_2 = 33 - 2*10 = 13$$ cm. If the horizontal segments are equal, $$b_1 = b_2 = 13/2 = 6.5$$ cm. Each cell is 2 cm, so $$6.5$$ cm is $$3.25$$ cells. The drawing shows the horizontal segments spanning 4 cells (8 cm). This conflicts with 6.5 cm. What if the '10 cm' refers to one of the horizontal segments? Say $$b_1 = 10$$ cm (5 cells). Then $$P = 10 + b_2 + 2s = 33$$. If it's an isosceles trapezoid, $$b_2$$ would be roughly the same as $$b_1$$, and $$s$$ would be different. But the drawing suggests the slanted sides are longer than the horizontal ones. Let's assume the figure is drawn such that the horizontal segments are indeed 4 cells (8 cm) long, and the slanted sides are 10 cm long. Then the perimeter is $$8 + 8 + 10 + 10 = 36$$ cm. This is not 33 cm. If we are supposed to move the red dots such that 'l' is the axis of symmetry, and the perimeter becomes 33 cm. Let the lengths of the parallel sides be $$b_1$$ and $$b_2$$, and the length of the non-parallel sides be $$s$$. So $$b_1 + b_2 + 2s = 33$$. Since 'l' is the axis of symmetry, if the parallel sides are horizontal, then the non-parallel sides must be equal, $$s$$. Let's assume the horizontal sides are of lengths $$b_1$$ and $$b_2$$. The drawing shows them spanning 4 cells, so let's assume they are $$b_1 = 8$$ cm and $$b_2 = 8$$ cm. Then $$8 + 8 + 2s = 33$$, which means $$16 + 2s = 33$$, so $$2s = 17$$, and $$s = 8.5$$ cm. This contradicts the '10 cm' label. What if the '10 cm' is correct for the slanted sides, so $$s = 10$$ cm. Then $$b_1 + b_2 + 2(10) = 33$$, so $$b_1 + b_2 = 13$$ cm. If the horizontal sides are equal due to symmetry, then $$b_1 = b_2 = 6.5$$ cm. Each cell is 2 cm, so 6.5 cm is 3.25 cells. This is possible if the red dots are not precisely on grid line intersections but can be moved freely, and the line 'l' is the axis of symmetry. The prompt says 'Move the red dots so that for the resulting quadrilateral, the line l becomes the axis of symmetry.' This implies we are supposed to adjust the positions. The '10 cm' label is given. And 'P = 33 cm' is given. Let's trust the '10 cm' label for the slanted side and the '33 cm' for the perimeter. Then the sum of the two slanted sides is $$2 \times 10 = 20$$ cm. The remaining perimeter for the two horizontal sides is $$33 - 20 = 13$$ cm. If these horizontal sides are equal due to symmetry, then each horizontal side must be $$13 / 2 = 6.5$$ cm. The grid cell size is 2 cm. So, a length of 6.5 cm corresponds to $$6.5 / 2 = 3.25$$ grid cells. This means the horizontal sides would span 3.25 cells. The slanted sides are 10 cm, which is $$10 / 2 = 5$$ cells. If the slanted sides are 5 cells long, and the horizontal sides are 3.25 cells long, and 'l' is the axis of symmetry, the figure would be an isosceles trapezoid. Let's check if this makes sense visually. The drawing shows the horizontal sides spanning 4 cells (8 cm), and the slanted sides are labeled 10 cm (5 cells). This would give a perimeter of $$8+8+10+10 = 36$$ cm. However, the problem asks us to move the red dots to make 'l' the axis of symmetry. The value '33 cm' is presented as P. It is highly probable that '33 cm' is the correct perimeter. And '10 cm' is the length of the slanted side. The grid is provided for context, but the actual positions of the red dots might need adjustment to achieve a perimeter of 33 cm with symmetry. So, assuming the intended configuration for a perimeter of 33 cm, with symmetry about line 'l', and slanted sides of 10 cm, then the two horizontal sides must sum to 13 cm, meaning each horizontal side is 6.5 cm. The cell size is 2 cm. Thus, each horizontal side is 3.25 cells long. This implies the drawing is illustrative, and the key information to solve the problem is: the shape is an isosceles trapezoid (due to symmetry about a vertical line 'l' and having horizontal bases), the non-parallel sides are 10 cm each, and the perimeter is 33 cm. The question implicitly asks to calculate the perimeter given these conditions, or verify the given perimeter. Since the question asks to