问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: How many distinct diagonals of a convex hexagon can be drawn?
A. 6
B. 8
C. 9
D. 36
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

C. 9

A convex hexagon has 6 vertices, and a diagonal is a line segment that connects two non-adjacent vertices. To find the number of distinct diagonals, we can use the formula:

Number of diagonals = Number of vertices × (Number of vertices - 3) / 2

Plugging in the values, we get:

Number of diagonals = 6 × (6 - 3) / 2
= 6 × 3 / 2
= 9

Therefore, there are 9 distinct diagonals that can be drawn in a convex hexagon.		 C
deepseekr1

To determine the number of distinct diagonals in a convex hexagon, we use the formula for diagonals in a polygon:
\[
\frac{n(n-3)}{2}
\]
where \( n \) is the number of sides. For a hexagon (\( n = 6 \)):
\[
\frac{6(6-3)}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9
\]

Alternatively, each vertex connects to 3 non-adjacent vertices, giving \( 6 \times 3 = 18 \). Since this counts each diagonal twice, divide by 2:
\[
\frac{18}{2} = 9
\]

**Answer: C**		 C
gpto1 C C
GPT-4o C. 9 C
llama3.1-70B-Instruct

To find the number of distinct diagonals in a convex hexagon, we can use a formula or count them manually.

A convex hexagon has 6 vertices. A diagonal is a line segment that connects two non-adjacent vertices.

Let's count the diagonals manually:

1. From vertex 1, we can draw 3 diagonals (to vertices 3, 4, and 5).
2. From vertex 2, we can draw 3 diagonals (to vertices 4, 5, and 6).
3. From vertex 3, we can draw 2 diagonals (to vertices 5 and 6).
4. From vertex 4, we can draw 2 diagonals (to vertices 6 and 1).
5. From vertex 5, we can draw 1 diagonal (to vertex 1).
6. From vertex 6, we can draw 1 diagonal (to vertex 2).

However, we have counted each diagonal twice (once from each endpoint). So, we need to divide the total count by 2.

The total count is: 3 + 3 + 2 + 2 + 1 + 1 = 12

Divide by 2: 12 / 2 = 6

But wait, we made a mistake! We didn't count the diagonals from vertex 1 to vertex 6, and from vertex 2 to vertex 5, and from vertex 3 to vertex 4. These are 3 additional diagonals.

So, the correct total count is: 6 + 3 = 9

The correct answer is C.		 C
llama3.1-405B-Instruct

C. 9.

A convex hexagon has 6 vertices. To draw a diagonal, we need to choose 2 vertices out of the 6. This can be done in 6C2 = 15 ways. However, this count includes the 6 sides of the hexagon, which are not considered diagonals. Therefore, we subtract 6 from 15 to get the number of distinct diagonals: 15 - 6 = 9.		 C
DeepSeek-Coder-V2 C. 9 C
Qwen2-72B-Instruct C. 9 C
baichuan4 C C
doubao C

A convex hexagon has 6 vertices. From each vertex, we can draw diagonals to 3 other vertices (excluding the vertex itself and the two adjacent vertices). Since there are 6 vertices, we multiply 6 by 3 and then divide by 2 to avoid double-counting. So, 6×3÷2 = 9 distinct diagonals.		 C
minimax To find the number of distinct diagonals in a convex hexagon, we can use the formula for the number of diagonals in any polygon, which is:

Number of diagonals = n(n - 3) / 2

where n is the number of sides in the polygon.

For a hexagon, n = 6. Plugging this into the formula gives us:

Number of diagonals = 6(6 - 3) / 2
= 6(3) / 2
= 18 / 2
= 9

So, the correct answer is:

C. 9		 C
kimi To find the number of distinct diagonals in a convex hexagon, you can use the formula for finding the number of diagonals in a polygon, which is:

Number of diagonals = n(n - 3) / 2

where n is the number of sides in the polygon.

For a hexagon, n = 6. Plugging this into the formula gives:

Number of diagonals = 6(6 - 3) / 2
Number of diagonals = 6 * 3 / 2
Number of diagonals = 18 / 2
Number of diagonals = 9

So the correct answer is C. 9.		 C
wenxinyiyan C

Explanation:
In a convex hexagon, there are 6 vertices. To draw a diagonal, we need to choose 2 vertices that are not adjacent.

1. Total number of ways to choose 2 vertices out of 6 is C(6, 2) = 15 (where C(n, k) is the combination of n items taken k at a time).

2. However, these 15 pairs include the 6 pairs of adjacent vertices, which do not form diagonals.

3. Therefore, the number of distinct diagonals is 15 - 6 = 9.

So, the answer is C.		 C
zhipu To determine the number of distinct diagonals in a convex hexagon, we can use the formula for the number of diagonals in an \( n \)-sided polygon, which is given by:

\[
\frac{n(n-3)}{2}
\]

For a hexagon, \( n = 6 \):

\[
\frac{6(6-3)}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9
\]

So, the number of distinct diagonals in a convex hexagon is 9.

The correct answer is C.		 C
gpto1 C C
deepseekv3 To determine the number of distinct diagonals in a convex hexagon, we can use the formula for the number of diagonals in an \( n \)-sided polygon:

\[
\text{Number of diagonals} = \frac{n(n - 3)}{2}
\]

For a hexagon, \( n = 6 \). Plugging this into the formula:

\[
\text{Number of diagonals} = \frac{6(6 - 3)}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9
\]

Thus, the correct answer is:

Answer: C		 C