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 coordinates of the points:
[tex]\[
A = (11, -5) \quad \text{and} \quad B = (1, 7)
\][/tex]
First, identify the coordinates:
[tex]\[
(x_1, y_1) = (11, -5)
\][/tex]
[tex]\[
(x_2, y_2) = (1, 7)
\][/tex]
Next, calculate the differences between the x-coordinates and y-coordinates:
[tex]\[
x_2 - x_1 = 1 - 11 = -10
\][/tex]
[tex]\[
y_2 - y_1 = 7 - (-5) = 7 + 5 = 12
\][/tex]
Now, square these differences:
[tex]\[
(x_2 - x_1)^2 = (-10)^2 = 100
\][/tex]
[tex]\[
(y_2 - y_1)^2 = 12^2 = 144
\][/tex]
Add these squared differences:
[tex]\[
(x_2 - x_1)^2 + (y_2 - y_1)^2 = 100 + 144 = 244
\][/tex]
Take the square root of the sum to find the distance [tex]\( d \)[/tex]:
[tex]\[
d = \sqrt{244} \approx 15.620499351813308
\][/tex]
Finally, round the distance to the nearest tenth:
[tex]\[
d \approx 15.6
\][/tex]
Thus, the distance between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is approximately [tex]\( 15.6 \)[/tex].
