Question

Use the distance formula to find the distance between points A and B, rounded to the nearest tenth (A -3,5 B 7,2). Responses 9.0 9.0 10.0 10.0 10.2 10.2 10.4

Answer 1

To find the distance between points \( A(-3, 5) \) and \( B(7, 2) \), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where \( (x_1, y_1) \) are the coordinates of point A, and \( (x_2, y_2) \) are the coordinates of point B.

Substituting the coordinates of points A and B into the formula:

- \( x_1 = -3 \)
- \( y_1 = 5 \)
- \( x_2 = 7 \)
- \( y_2 = 2 \)

Calculating the differences:

\[
x_2 - x_1 = 7 - (-3) = 7 + 3 = 10
\]
\[
y_2 - y_1 = 2 - 5 = -3
\]

Now plug these values into the distance formula:

\[
d = \sqrt{(10)^2 + (-3)^2}
\]
\[
d = \sqrt{100 + 9}
\]
\[
d = \sqrt{109}
\]

Calculating \( \sqrt{109} \):

\[
\sqrt{109} \approx 10.4403
\]

Rounding to the nearest tenth, we get:

\[
d \approx 10.4
\]

Thus, the distance between points A and B is approximately **10.4**.