To find the distance between the points [tex]\( K(9, 2) \)[/tex] and [tex]\( L(-3, 9) \)[/tex], we use the distance formula:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Let's proceed step by step:
1. Identify the coordinates of the two points:
- [tex]\( K \)[/tex] has coordinates [tex]\( (x_1, y_1) = (9, 2) \)[/tex]
- [tex]\( L \)[/tex] has coordinates [tex]\( (x_2, y_2) = (-3, 9) \)[/tex]
2. Calculate the difference in the [tex]\( x \)[/tex]-coordinates and the [tex]\( y \)[/tex]-coordinates:
[tex]\[ \Delta x = x_2 - x_1 = -3 - 9 = -12 \][/tex]
[tex]\[ \Delta y = y_2 - y_1 = 9 - 2 = 7 \][/tex]
3. Square each difference:
[tex]\[ (\Delta x)^2 = (-12)^2 = 144 \][/tex]
[tex]\[ (\Delta y)^2 = 7^2 = 49 \][/tex]
4. Sum the squares of the differences:
[tex]\[ (\Delta x)^2 + (\Delta y)^2 = 144 + 49 = 193 \][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{193} \approx 13.892443989449804 \][/tex]
6. Round the distance to the nearest tenth:
[tex]\[ d \approx 13.9 \][/tex]
Therefore, the distance between points [tex]\( K(9, 2) \)[/tex] and [tex]\( L(-3, 9) \)[/tex], rounded to the nearest tenth, is:
[tex]\[ \boxed{13.9} \][/tex]
