Question

Find the distance between Upper F and Upper G.
font size increased by 2 0font size increased by 2 4font size increased by 2 8font size increased by 2 4font size increased by 2 yfont size increased by 2 xfont size increased by 8 Upper F left parenthesis 6 comma 8 right parenthesisfont size increased by 8 Upper G left parenthesis 16 comma 12 right parenthesisfont size increased by 2 8font size increased by 2 12font size increased by 2 16font size increased by 2 12font size increased by 2 16font size increased by 2 0



x y graph
Question content area bottom
Part 1
The distance between Upper F and Upper G is
  
enter your response here.
​(Type an exact answer using radicals as​ needed.)

Answer 1

To find the distance between the points \( F(6, 8) \) and \( G(16, 12) \), we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In our case:
- \( (x_1, y_1) = (6, 8) \)
- \( (x_2, y_2) = (16, 12) \)

Now we can plug these values into the formula:

\[
d = \sqrt{(16 - 6)^2 + (12 - 8)^2}
\]
\[
d = \sqrt{(10)^2 + (4)^2}
\]
\[
d = \sqrt{100 + 16}
\]
\[
d = \sqrt{116}
\]
\[
d = \sqrt{4 \times 29}
\]
\[
d = 2\sqrt{29}
\]

Therefore, the distance between points \( F \) and \( G \) is \( 2\sqrt{29} \).