geometry drawing task
requirements: draw on 1cm grid paper, define the coordinate system with grid point o as the origin (0,0) (x-axis right horizontally, y-axis up vertically), label all key measurements/calculations clearly in the blank, and fill the required parts completely.

draw the pattern as follows: 1. use coordinate formulas to draw the house: the body is a rectangle defined by 0≤x≤8, 0≤y≤6 (8cm×6cm), label its top side endpoints b(8,6) and c(0,6); the roof is an isosceles triangle defined by vertices b(8,6), c(0,6) and d(4,10) (height 4cm), shade the triangle completely. add a square window on the house body with the formula 1≤x≤3, 3≤y≤5 (2cm×2cm), and a rectangular door with 3≤x≤5, 0≤y≤4 (2cm×4cm) on the bottom edge, label the door’s upper vertices g(3,4) and h(5,4). 2. locate the heart’s center m(3,4) inside the house, draw a solid heart centered at m using the parametric formula: x = 2 cos³ t, y = 2 sin t - 1.25 (scaled to 4cm wide horizontally, 5cm tall vertically), fill the heart entirely and label its size. 3. inside the house next to the heart, draw a simple dog (height ≤3cm) with glasses on its face (use line segments/arcs for a clear outline). 4. mark points s (on roof peak d), v (on the heart’s top), i (on the dog’s ear) at key positions of the pattern, ensure points s, o, v, i are clearly labeled with capital letters.

用 latex 语言写这个几何画图题的题目描述 →
4. |

Question

geometry drawing task
requirements: draw on 1cm grid paper, define the coordinate system with grid point o as the origin (0,0) (x-axis right horizontally, y-axis up vertically), label all key measurements/calculations clearly in the blank, and fill the required parts completely.

draw the pattern as follows: 1. use coordinate formulas to draw the house: the body is a rectangle defined by 0≤x≤8, 0≤y≤6 (8cm×6cm), label its top side endpoints b(8,6) and c(0,6); the roof is an isosceles triangle defined by vertices b(8,6), c(0,6) and d(4,10) (height 4cm), shade the triangle completely. add a square window on the house body with the formula 1≤x≤3, 3≤y≤5 (2cm×2cm), and a rectangular door with 3≤x≤5, 0≤y≤4 (2cm×4cm) on the bottom edge, label the door’s upper vertices g(3,4) and h(5,4). 2. locate the heart’s center m(3,4) inside the house, draw a solid heart centered at m using the parametric formula: x = 2 cos³ t, y = 2 sin t - 1.25 (scaled to 4cm wide horizontally, 5cm tall vertically), fill the heart entirely and label its size. 3. inside the house next to the heart, draw a simple dog (height ≤3cm) with glasses on its face (use line segments/arcs for a clear outline). 4. mark points s (on roof peak d), v (on the heart’s top), i (on the dog’s ear) at key positions of the pattern, ensure points s, o, v, i are clearly labeled with capital letters.

用 latex 语言写这个几何画图题的题目描述 →
4. |

Accepted Answer

To write the given geometry drawing task in LaTeX, we can use the `article` document class and the `tikz` package for drawing (though the task is more about the description, we can format the text with LaTeX commands for structure and math notation). Here is the LaTeX code:

```latex
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}

\section*{Geometry Drawing Task}

\textbf{Requirements:} Draw on 1cm grid paper, define the coordinate system with grid point $ O $ as the origin $ (0,0) $ ($ x $-axis right horizontally, $ y $-axis up vertically), label all key measurements/calculations clearly, and fill the required parts completely.

\subsection*{Drawing the Pattern}
\begin{enumerate}
    \item \textbf{Draw the house:}
    \begin{itemize}
        \item The body is a rectangle defined by $ 0 \leq x \leq 8 $, $ 0 \leq y \leq 6 $ (8cm$\times$6cm). Label its top side endpoints $ B(8,6) $ and $ C(0,6) $.
        \item The roof is an isosceles triangle defined by vertices $ B(8,6) $, $ C(0,6) $ and $ D(4,10) $ (height 4cm). \textbf{Shade the triangle completely}.
        \item Add a square window on the house body with the formula $ 1 \leq x \leq 3 $, $ 3 \leq y \leq 5 $ (2cm$\times$2cm).
        \item Add a rectangular door with $ 3 \leq x \leq 5 $, $ 0 \leq y \leq 4 $ (2cm$\times$4cm) on the bottom edge. Label the door's upper vertices $ G(3,4) $ and $ H(5,4) $.
    \end{itemize}
    \item \textbf{Draw the heart:}
    \begin{itemize}
        \item Locate the heart's center $ M(3,4) $ inside the house.
        \item Draw a \textbf{solid heart} centered at $ M $ using the parametric formula:
        $$
        x = 2\cos^{3}t, \quad y = 2\sin t - 1.25
        $$
        (scaled to 4cm wide horizontally, 5cm tall vertically). \textbf{Fill the heart entirely} and label its size.
    \end{itemize}
    \item \textbf{Draw the dog:} Inside the house next to the heart, draw a simple dog (height $\leq 3$cm) with \textbf{glasses on its face} (use line segments/arcs for a clear outline).
    \item \textbf{Mark key points:} Mark points $ S $ (on roof peak $ D $), $ V $ (on the heart's top), $ I $ (on the dog's ear) at key positions of the pattern. Ensure points $ S $, $ O $, $ V $, $ I $ are clearly labeled with capital letters.
\end{enumerate}

\end{document}
```

This LaTeX code structures the geometry drawing task with appropriate sectioning, math notation, and formatting to match the original problem description.

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