Mid points of the sides Ab and AC of a `DeltaABC` are (3,5) and (-3,-3) respectively, then the length of the side BC is

Options

A. 10
B. 20
C. 15
D. 30

Answer

To solve the problem, we need to find the length of side BC of triangle ABC given the midpoints of sides AB and AC.

### Step-by-Step Solution:

1. **Identify the Midpoints**:
Let M be the midpoint of side AB, and N be the midpoint of side AC. We are given:
- M (3, 5)
- N (-3, -3)

2. **Use the Midpoint Theorem**:
According to the midpoint theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half its length. Therefore, MN is parallel to BC and MN = 1/2 * BC.

3. **Calculate the Length of MN**:
We can find the length of segment MN using the distance formula:
\[ MN = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of M and N:
\[ MN = \sqrt{((-3) - 3)^2 + ((-3) - 5)^2} \]
\[ = \sqrt{(-6)^2 + (-8)^2} \]
\[ = \sqrt{36 + 64} \]
\[ = \sqrt{100} = 10 \]

4. **Find the Length of BC**:
Since MN is half the length of BC, we can find BC:
\[ BC = 2 \times MN = 2 \times 10 = 20 \]

### Final Answer:
The length of side BC is **20**.