To find the distance [tex]\( d \)[/tex] between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we use the distance formula:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Given the points [tex]\( A = (-7, -7) \)[/tex] and [tex]\( B = (-3, -1) \)[/tex], we identify the coordinates as follows:
[tex]\[
(x_1, y_1) = (-7, -7)
\][/tex]
[tex]\[
(x_2, y_2) = (-3, -1)
\][/tex]
First, subtract the corresponding coordinates of points [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[
x_2 - x_1 = -3 - (-7) = -3 + 7 = 4
\][/tex]
[tex]\[
y_2 - y_1 = -1 - (-7) = -1 + 7 = 6
\][/tex]
Next, square these differences:
[tex]\[
(x_2 - x_1)^2 = 4^2 = 16
\][/tex]
[tex]\[
(y_2 - y_1)^2 = 6^2 = 36
\][/tex]
Now, add these squared values:
[tex]\[
16 + 36 = 52
\][/tex]
Take the square root of this sum to find the distance:
[tex]\[
d = \sqrt{52} \approx 7.211102550927978
\][/tex]
Finally, round the distance to the nearest tenth:
[tex]\[
d \approx 7.2
\][/tex]
Thus, the distance [tex]\( d \)[/tex] between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is approximately 7.2 units.
