Question

geometry drawing task
word to form: sovi (using points s, o, v, i)
requirements: draw on 1cm grid paper, label all key measurements clearly, write necessary calculations in the blank space.
draw a complete pattern as required: take grid point o (one of the four letters) as the bottom - left vertex of a house, draw the house with an 8cm long and 6cm wide rectangle oabc as the body; above the rectangle, take bc as the base to draw an isosceles triangle bcd (roof, height 4cm) and shade the roof completely. draw a 4cm tall and 2cm wide small rectangle as the door on the houses bottom edge oa, with its center aligned to the houses vertical midline, label the doors bottom - left vertex e and bottom - right f, upper vertices g and h. locate point m inside the house (3cm from oc, 4cm from oa), mark m with a cross (×) and label the distances; with m as the center, draw a 4cm wide (horizontal) and 5cm tall (vertical) solid heart (fill it completely) by drawing two upward quarter - circles (centers 1cm left/right of m, radius 1cm) for the upper part, connecting the circle bottoms to 2.5cm below m (2cm left/right) with line segments, then joining the segment ends for the lower part, label the hearts size. inside the house, next to the solid heart, draw a simple dog (height ≤3cm) with glasses on its face (use line segments and arcs for clear outline). finally, mark points s, v, i (matching the sovi word with point o) at three different key positions on the pattern (e.g., s on the roof peak d, v on the hearts top, i on the dogs ear), ensure the four points s, o, v, i are clearly labeled and form the word sovi.

Explanation:

Step1: Set up coordinate system with O at (0,0)

Since O is the bottom - left vertex, let's place O at the origin \((0,0)\) of a coordinate system on the 1cm grid paper. The rectangle OABC has length 8cm (along the x - axis) and width 6cm (along the y - axis). So, the coordinates of the vertices of the rectangle: \(O=(0,0)\), \(A=(8,0)\), \(B=(8,6)\), \(C=(0,6)\).

Step2: Draw the isosceles triangle BCD (roof)

The base \(BC\) of the triangle is the same as the top side of the rectangle OABC, so the length of \(BC = 8cm\). The height of the isosceles triangle is 4cm. The mid - point of \(BC\) is at \((4,6)\) (since \(B=(8,6)\) and \(C=(0,6)\), the mid - point \(x\) - coordinate is \(\frac{8 + 0}{2}=4\), \(y\) - coordinate is 6). The peak \(D\) of the triangle will be at \((4,6 + 4)=(4,10)\) (since we move 4cm above the mid - point of \(BC\)).

Step3: Draw the door (small rectangle)

The door is 4cm tall and 2cm wide, with its center aligned to the vertical mid - line of the house. The vertical mid - line of the house (rectangle OABC) is at \(x=\frac{8}{2}=4\) (since the length of OA is 8cm). The width of the door is 2cm, so the left - most \(x\) - coordinate of the door is \(4-\frac{2}{2}=3\) and the right - most \(x\) - coordinate is \(4+\frac{2}{2}=5\). The height of the door is 4cm, and it is on the bottom edge OA (where \(y = 0\)), so the bottom vertices of the door: \(E=(3,0)\), \(F=(5,0)\) and the upper vertices: \(G=(3,4)\), \(H=(5,4)\).

Step4: Locate point M

Point M is 3cm from OC (OC is the left - hand side of the rectangle, along the y - axis, \(x = 0\)) and 4cm from OA (OA is the bottom edge, along the x - axis, \(y = 0\)). So, the \(x\) - coordinate of M is 3 (since it is 3cm from \(x = 0\)) and the \(y\) - coordinate of M is 4 (since it is 4cm from \(y = 0\)). Thus, \(M=(3,4)\).

Step5: Draw the solid heart

The heart is centered at M \((3,4)\), 4cm wide (horizontal) and 5cm tall (vertical). The upper part consists of two upward quarter - circles with centers 1cm left/right of M. The center of the left quarter - circle is \((3 - 1,4)=(2,4)\) and the center of the right quarter - circle is \((3+1,4)=(4,4)\), and the radius of each quarter - circle is 1cm. The bottom of the quarter - circles is at \(y = 4\) (since the radius is 1cm, the bottom of the quarter - circles (which are upward - facing) is at \(y=4\)). We need to connect the circle bottoms to 2.5cm below M. The \(y\) - coordinate of the points 2.5cm below M is \(4-2.5 = 1.5\). The left - most \(x\) - coordinate of the lower part is \(3 - 2=1\) (since the horizontal width of the lower part is 2cm left/right from the center) and the right - most \(x\) - coordinate is \(3 + 2 = 5\). So, we connect \((2,4)\) to \((1,1.5)\) and \((4,4)\) to \((5,1.5)\), and then connect \((1,1.5)\) to \((5,1.5)\).

Step6: Draw the simple dog

Draw a simple dog with height \(\leq3cm\) next to the solid heart. For example, we can draw the dog's body as a small rectangle or an irregular shape, and the face with glasses (using line segments and arcs). Let's say the dog's body is a rectangle with length 3cm and height 2cm, centered at a suitable position next to the heart (e.g., centered at \((6,3)\) with length 3cm (x - range from 4.5 to 7.5) and height 2cm (y - range from 1 to 3)). The glasses can be two small arcs or rectangles on the face.

Step7: Label points S, V, I

We can label \(S = D=(4,10)\) (roof peak), \(O=(0,0)\) (bottom - left of the house), \(V\) at the top of the heart (the top of the heart is at the top of the two quarter - circles. The top of a quarter - circle with center \((2,4)\) and radius 1cm is at \((2,4 + 1)=(2,5)\), and the top of the quarter - circle with center \((4,4)\) and radius 1cm is at \((4,4 + 1)=(4,5)\). The top of the heart is the mid - point of these two tops, so \(V=(3,5)\)), and \(I\) on the dog's ear (e.g., if the dog's ear is at \((7,4)\), we can label \(I=(7,4)\)).

Answer:

The drawing is completed following the above - mentioned steps, with all key measurements labeled, the roof shaded, the heart and dog drawn, and points S, O, V, I labeled to form the word SOVI. The final drawing will have:

• Rectangle OABC: \(O=(0,0)\), \(A=(8,0)\), \(B=(8,6)\), \(C=(0,6)\)
• Triangle BCD: \(B=(8,6)\), \(C=(0,6)\), \(D=(4,10)\)
• Door EFGH: \(E=(3,0)\), \(F=(5,0)\), \(G=(3,4)\), \(H=(5,4)\)
• Point M: \((3,4)\)
• Heart with key points as calculated
• Dog with height \(\leq3cm\) and glasses
• Points S, V, I labeled as \(S=(4,10)\), \(O=(0,0)\), \(V=(3,5)\), \(I=(7,4)\) (example positions)