6) Point $$ M $$ is the midpoint of $$ A B $$. If the coordinates of $$ M $$ are $$ (2,8) $$ and the coordinates of $$ B $$ are $$ (10,12) $$, what are the coordinates of $$ A $$ ? 7) $$ M $$ is the midpoint of $$ A B $$. If the coordinates of $$ A $$ are $$ (-1,5) $$ and the coordinates of $$ B $$ are $$ (3,3) $$, what are the coordinates of $$ M $$ ?

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**6) Finding the Coordinates of $$ A $$:**

- Since $$ M $$ is the midpoint of $$ AB $$, the midpoint formula states:
  $$
  M = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
  $$
- Given that $$ M = (2,8) $$ and $$ B = (10,12) $$, we set up the equations:
  $$
  2 = \frac{x_A + 10}{2} \quad \text{and} \quad 8 = \frac{y_A + 12}{2}
  $$
- **Solving for $$ x_A $$:**
  $$
  2 = \frac{x_A + 10}{2} \quad \Rightarrow \quad 4 = x_A + 10 \quad \Rightarrow \quad x_A = 4 - 10 = -6
  $$
- **Solving for $$ y_A $$:**
  $$
  8 = \frac{y_A + 12}{2} \quad \Rightarrow \quad 16 = y_A + 12 \quad \Rightarrow \quad y_A = 16 - 12 = 4
  $$
- **Answer:** The coordinates of $$ A $$ are $$ (-6, 4) $$.

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**7) Finding the Coordinates of $$ M $$:**

- For the midpoint $$ M $$ of $$ AB $$ with $$ A = (-1,5) $$ and $$ B = (3,3) $$, the midpoint formula is:
  $$
  M = \left( \frac{-1 + 3}{2}, \frac{5 + 3}{2} \right)
  $$
- **Calculating the coordinates:**
  $$
  \frac{-1+3}{2} = \frac{2}{2} = 1 \quad \text{and} \quad \frac{5+3}{2} = \frac{8}{2} = 4
  $$
- **Answer:** The coordinates of $$ M $$ are $$ (1, 4) $$.
**6) Coordinates of $$ A $$:** $$ A = (-6, 4) $$ **7) Coordinates of $$ M $$:** $$ M = (1, 4) $$

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