To find the distance between the points [tex]\( K(9, 2) \)[/tex] and [tex]\( L(-3, 9) \)[/tex], we 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]\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's apply this formula step by step to our given points [tex]\( K(9, 2) \)[/tex] and [tex]\( L(-3, 9) \)[/tex]:
1. Assign the coordinates:
[tex]\[
x_1 = 9, \quad y_1 = 2, \quad x_2 = -3, \quad y_2 = 9
\][/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[
\text{Distance} = \sqrt{((-3) - 9)^2 + (9 - 2)^2}
\][/tex]
3. Simplify the expressions inside the square root:
[tex]\[
(-3 - 9) = -12, \quad (9 - 2) = 7
\][/tex]
[tex]\[
\text{Distance} = \sqrt{(-12)^2 + (7)^2}
\][/tex]
4. Square the numbers:
[tex]\[
(-12)^2 = 144, \quad 7^2 = 49
\][/tex]
[tex]\[
\text{Distance} = \sqrt{144 + 49}
\][/tex]
5. Add the squared numbers:
[tex]\[
\text{Distance} = \sqrt{193}
\][/tex]
6. Calculate the square root of 193:
[tex]\[
\text{Distance} \approx 13.892443989449804
\][/tex]
7. Round the distance to the nearest tenth:
[tex]\[
\text{Distance} \approx 13.9
\][/tex]
So, the distance between the points [tex]\( K(9, 2) \)[/tex] and [tex]\( L(-3, 9) \)[/tex] to the nearest tenth is:
13.9
Hence, the correct answer is:
13.9
