To find the distance between the points [tex]\( K(-1, -3) \)[/tex] and [tex]\( L(0, 0) \)[/tex], we'll use the distance formula, which is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here's the step-by-step process:
1. Identify the coordinates of the points:
[tex]\[ K(x_1, y_1) = (-1, -3) \][/tex]
[tex]\[ L(x_2, y_2) = (0, 0) \][/tex]
2. Calculate the differences in the x-coordinates and y-coordinates:
[tex]\[ \Delta x = x_2 - x_1 = 0 - (-1) = 1 \][/tex]
[tex]\[ \Delta y = y_2 - y_1 = 0 - (-3) = 3 \][/tex]
3. Square the differences:
[tex]\[ (\Delta x)^2 = 1^2 = 1 \][/tex]
[tex]\[ (\Delta y)^2 = 3^2 = 9 \][/tex]
4. Sum the squares of the differences:
[tex]\[ (\Delta x)^2 + (\Delta y)^2 = 1 + 9 = 10 \][/tex]
5. Take the square root of the sum to find the distance:
[tex]\[ d = \sqrt{10} \approx 3.1622776601683795 \][/tex]
6. Round the distance to the nearest tenth:
The distance [tex]\( d \approx 3.2 \)[/tex]
Therefore, the distance between the points [tex]\( K(-1, -3) \)[/tex] and [tex]\( L(0, 0) \)[/tex] is approximately [tex]\( 3.2 \)[/tex] units when rounded to the nearest tenth.
