To find the distance, [tex]\( d \)[/tex], between two points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] in the coordinate plane, you can use the distance formula. The distance formula for two points [tex]\( A(x_1, y_1) \)[/tex] and [tex]\( B(x_2, y_2) \)[/tex] is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given the points:
[tex]\[ A = (-2, -10) \][/tex]
[tex]\[ B = (-6, 0) \][/tex]
Let's denote the coordinates as follows:
[tex]\[
x_1 = -2, \quad y_1 = -10
\][/tex]
[tex]\[
x_2 = -6, \quad y_2 = 0
\][/tex]
Now, substitute these values into the distance formula:
1. Calculate [tex]\( (x_2 - x_1) \)[/tex] and [tex]\( (y_2 - y_1) \)[/tex]:
[tex]\[ x_2 - x_1 = -6 - (-2) = -6 + 2 = -4 \][/tex]
[tex]\[ y_2 - y_1 = 0 - (-10) = 0 + 10 = 10 \][/tex]
2. Square each of the results:
[tex]\[ (x_2 - x_1)^2 = (-4)^2 = 16 \][/tex]
[tex]\[ (y_2 - y_1)^2 = (10)^2 = 100 \][/tex]
3. Add the squared results:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 16 + 100 = 116 \][/tex]
4. Take the square root of the sum:
[tex]\[ d = \sqrt{116} \approx 10.770329614269007 \][/tex]
5. Round the result to the nearest tenth:
[tex]\[ d \approx 10.8 \][/tex]
Therefore, the distance [tex]\( d \)[/tex] between point [tex]\( A \)[/tex] and point [tex]\( B \)[/tex] rounded to the nearest tenth is:
[tex]\[ d \approx 10.8 \][/tex]
