Geometric and Spatial Reasoning Flashcards

What is the slope of a line that passes through the points (2, 3) and (6, 11)?

Answer: 2

Slope = (y₂ − y₁) / (x₂ − x₁) = (11 − 3) / (6 − 2) = 8 / 4 = 2.

A square has a perimeter of 36 cm. What is its area?

Answer: 81 cm²

Each side = 36 ÷ 4 = 9 cm, so area = 9² = 81 cm².

What is the surface area of a cube with a side length of 4?

Answer: 96

A cube has 6 faces, each with area 4² = 16, so surface area = 6 × 16 = 96.

Lines that lie in the same plane and never intersect are called:

Answer: Parallel lines

Parallel lines are coplanar lines that never meet, maintaining a constant distance apart.

If an angle measures 42°, what is the measure of its complementary angle?

Answer: 48°

Complementary angles sum to 90°, so the complement = 90° − 42° = 48°.

What is the distance between the points (1, 2) and (4, 6)?

Answer: 5

Distance = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5.

What is the area of a trapezoid with parallel bases of 6 and 10, and a height of 4?

Answer: 32

Area of a trapezoid = ½(b₁ + b₂) × h = ½(6 + 10) × 4 = ½ × 16 × 4 = 32.