To determine the distance between two points [tex]\( G(13, 2) \)[/tex] and [tex]\( H(1, 7) \)[/tex], Clint needs to use the distance formula. The distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Plugging in the coordinates [tex]\( G(13, 2) \)[/tex] and [tex]\( H(1, 7) \)[/tex]:
[tex]\[
d = \sqrt{(1 - 13)^2 + (7 - 2)^2}
\][/tex]
Let's break down the terms inside the square root:
1. Calculate [tex]\( (x_2 - x_1) \)[/tex]:
[tex]\[
1 - 13 = -12
\][/tex]
Then, square this result:
[tex]\[
(-12)^2 = 144
\][/tex]
2. Calculate [tex]\( (y_2 - y_1) \)[/tex]:
[tex]\[
7 - 2 = 5
\][/tex]
Then, square this result:
[tex]\[
5^2 = 25
\][/tex]
Now, sum the squared differences:
[tex]\[
144 + 25 = 169
\][/tex]
Finally, take the square root of the sum:
[tex]\[
d = \sqrt{169} = 13
\][/tex]
Thus, the expression Clint uses is:
[tex]\[
\sqrt{(7-2)^2 + (1-13)^2}
\][/tex]
So the correct choice among the given options is:
[tex]\[
\sqrt{(7-2)^2+(1-13)^2}
\][/tex]
Thus, Clint will use the expression:
[tex]\[
\sqrt{(7 - 2)^2 + (1 - 13)^2}
\][/tex]
