Question

ap geometry – constructed response question
total score: 10 points | time allowed: 15 minutes
materials: 1 cm grid paper, colored pencils/markers (brown, light gray, blue, red, black), ruler, pencil
directions: on 1 cm grid paper, perform a precise geometric construction that includes a house, solid heart, and simple puppy with glasses, following all color, fill, dimension, and labeling rules below; label all key linear dimensions directly on the figure, fill specified regions completely, and clearly mark the greek letters α, β, γ, δ at the required positions (partial credit for correct partial constructions). construct an 8 cm × 6 cm rectangular house body with a brown outline, topped with an isosceles triangle roof (3 cm height) that has the rectangle’s top side as its base and is fully filled with light gray; on the left middle of the rectangular body, draw a 2 cm side - length square window with a blue outline, and on the lower middle of the rectangular body, draw a 2 cm × 4 cm rectangular door with a black outline. inside the house, to the right of the window, construct a 4 cm (horizontal) × 4 cm (vertical) solid heart fully filled with red (label its width/height); adjacent to the red heart (lower position inside the house), draw a simple geometric puppy (total height ≤ 3 cm) with a black outline and add small round glasses on its face with a blue frame outline. mark α at the roof triangle’s apex, β at the square window’s center, γ at the red heart’s top vertex, and δ at the puppy’s head top, with all greek letter labels clearly placed next to their respective points.

Explanation:

Step1: Prepare Grid Paper

Get 1 cm grid paper. This will help in precise geometric construction as each grid square is 1 cm, making it easy to measure lengths.

Step2: Construct House Body

Draw a rectangle with length 8 cm (8 grid squares) and height 6 cm (6 grid squares) for the house body. Outline it with brown.

Step3: Construct Roof

The roof is an isosceles triangle with base equal to the top side of the rectangle (8 cm) and height 3 cm (3 grid squares). The base is the top side of the rectangle, so the apex is 3 cm above the top side. Fill the triangle with light gray.

Step4: Construct Window

On the left middle of the rectangular body, draw a square with side - length 2 cm (2 grid squares). Outline it with blue.

Step5: Construct Door

On the lower middle of the rectangular body, draw a rectangle with dimensions 2 cm×4 cm (2 grid squares by 4 grid squares). Outline it with black.

Step6: Construct Solid Heart

Inside the house, to the right of the window, construct a 4 cm×4 cm solid heart. A heart can be constructed by combining two semicircles on top of a square or using a more traditional heart - shape construction (e.g., two overlapping circles or a square with curved top). Fill it with red and label its width and height as 4 cm.

Step7: Construct Puppy with Glasses

Adjacent to the red heart (lower position inside the house), draw a simple geometric puppy with a total height ≤ 3 cm. The puppy can be made of simple shapes like a circle for the head, rectangles for the body and legs, and triangles for the ears. Add small round glasses (circles) on its face with a blue frame outline. The outline of the puppy is black.

Step8: Mark Greek Letters

• Mark α at the roof triangle’s apex.
• Mark β at the square window’s center (the center of a 2×2 square is at (1,1) if the square starts at (0,0) in a local coordinate system).
• Mark γ at the red heart’s top vertex.
• Mark δ at the puppy’s head top.

Answer:

The geometric construction is completed following the above - mentioned steps, with all the required shapes, colors, and labels as specified.