Question

What is the distance from point A to point B? Round your answer to the nearest tenth.
Coordinate A (-3,5)
Coordinate B(7,2)
What is the midpoint of line segment AB

Answer 1

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

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

Here, \((x_1, y_1) = (-3, 5)\) and \((x_2, y_2) = (7, 2)\).

Now substituting the coordinates into the formula:

\[
d = \sqrt{(7 - (-3))^2 + (2 - 5)^2}
\]
\[
d = \sqrt{(7 + 3)^2 + (2 - 5)^2}
\]
\[
d = \sqrt{(10)^2 + (-3)^2}
\]
\[
d = \sqrt{100 + 9}
\]
\[
d = \sqrt{109}
\]

Calculating \(\sqrt{109}\):

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

Rounding to the nearest tenth, the distance from point A to point B is:

\[
\text{Distance} \approx 10.4
\]

Next, to find the midpoint of line segment AB, we can use the midpoint formula:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Substituting the coordinates:

\[
\text{Midpoint} = \left( \frac{-3 + 7}{2}, \frac{5 + 2}{2} \right)
\]
\[
\text{Midpoint} = \left( \frac{4}{2}, \frac{7}{2} \right)
\]
\[
\text{Midpoint} = (2, 3.5)
\]

Thus, the midpoint of line segment AB is:

\[
\text{Midpoint} = (2, 3.5)
\]

In summary:
- The distance from point A to point B is approximately **10.4**.
- The midpoint of line segment AB is **(2, 3.5)**.