The midpoint of $$ (2, a) $$ and $$ (b, 7) $$ is $$ (4,5) $$. The values of $$ a $$ and $$ b $$ are respectively

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To find the values of $$ a $$ and $$ b $$ given that the midpoint of the points $$ (2, a) $$ and $$ (b, 7) $$ is $$ (4, 5) $$, we can use the midpoint formula:

$$
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$$

Applying this to the given points:

$$
\left( \frac{2 + b}{2}, \frac{a + 7}{2} \right) = (4, 5)
$$

This gives us two equations:

1. For the $$ x $$-coordinates:
$$
\frac{2 + b}{2} = 4
$$
Multiply both sides by 2:
$$
2 + b = 8 \implies b = 6
$$

2. For the $$ y $$-coordinates:
$$
\frac{a + 7}{2} = 5
$$
Multiply both sides by 2:
$$
a + 7 = 10 \implies a = 3
$$

**Therefore, the values are $$ a = 3 $$ and $$ b = 6 $$.**

Answer: $$ a = 3 $$ and $$ b = 6 $$
$$ a = 3 $$ and $$ b = 6 $$.

The midpoint of and is . The values of and are respectively

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