Question

Question 39
An object starts moving from point A and continues along a straight path from A to point D.
the main points are
A(0,0)
B(3,30)
C(6,30)
D(11,0)
If the object starts moving from point A and continues along a straight path from point A to point D, which of the following is true?

a
In the interval from point C to point D, the object travels 0 m.
b
In the interval from point A to point D, the object travels 11 m.
c
In the interval from point A to point B, the object travels 30 m.
d
In the interval from point B to point C, the object travels 30 m.

Answer 1

To analyze the movement of the object from point A to point D based on the given points, let's break down the distances correctly.

1. **Points A, B, C, and D:**
- A(0, 0)
- B(3, 30)
- C(6, 30)
- D(11, 0)

2. **Distance Calculations:**
- **From A to B:** The distance can be calculated using the distance formula:
\[
\text{Distance (A to B)} = \sqrt{(3-0)^2 + (30-0)^2} = \sqrt{3^2 + 30^2} = \sqrt{9 + 900} = \sqrt{909} \approx 30.15 \, m
\]

- **From B to C:**
Since B and C are horizontally aligned (same y-coordinate), the distance can be calculated as:
\[
\text{Distance (B to C)} = C_x - B_x = 6 - 3 = 3 \, m
\]

- **From C to D:**
Similar to above, since C and D are also diagonally positioned, we have:
\[
\text{Distance (C to D)} = \sqrt{(11-6)^2 + (0-30)^2} = \sqrt{5^2 + (-30)^2} = \sqrt{25 + 900} = \sqrt{925} \approx 30.41 \, m
\]

- **From A to D:**
Lastly, the distance from A to D:
\[
\text{Distance (A to D)} = \sqrt{(11-0)^2 + (0-0)^2} = \sqrt{11^2} = 11 \, m
\]

3. **Evaluating the Options:**
- **(a)** In the interval from point C to point D, the object travels 0 m.
- **False** (the distance is \(\approx 30.41\) m).

- **(b)** In the interval from point A to point D, the object travels 11 m.
- **True** (correct as per our calculations).

- **(c)** In the interval from point A to point B, the object travels 30 m.
- **False** (it travels approximately 30.15 m).

- **(d)** In the interval from point B to point C, the object travels 30 m.
- **False** (the distance is 3 m).

Based on all the calculations, the only true statement is:

**b.** In the interval from point A to point D, the object travels 11 m.