Answer :
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]
[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]
