What is the value of $$ r $$ if the midpoent bethecen the points $$ [4,2] $$ and $$ [1, r] $$ is $$ \left[\frac{5}{2}, \frac{9}{2}\right] $$

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To find the value of $$ r $$ such that the midpoint between the points $$(4, 2)$$ and $$(1, r)$$ is $$\left(\frac{5}{2}, \frac{9}{2}\right)$$, we can use the midpoint formula:

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

Given the points $$(4, 2)$$ and $$(1, r)$$, the midpoint is:

$$
\left( \frac{4 + 1}{2}, \frac{2 + r}{2} \right) = \left( \frac{5}{2}, \frac{2 + r}{2} \right)
$$

We know the midpoint is $$\left(\frac{5}{2}, \frac{9}{2}\right)$$. Therefore, we can set up the following equation for the y-coordinates:

$$
\frac{2 + r}{2} = \frac{9}{2}
$$

Solve for $$ r $$:

$$
2 + r = 9 \quad \Rightarrow \quad r = 9 - 2 \quad \Rightarrow \quad r = 7
$$

**Answer:** $$ r = 7 $$
$$ r = 7 $$

What is the value of if the midpoent
bethecen the points and is

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What is the value of if the midpoent bethecen the points and is