Question

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Question 1
(1 point)
What is the distance from point A to point B? Round your answer to the nearest tenth.
point A is at (-3,5) and Point B is at (7,2)
units

Question 2
(1 point)
What is the midpoint of line segment AB?

(
,
) Enter your answer as a decimal if necessary.

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Answer 1

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

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

Where:
- \((x_1, y_1) = (-3, 5)\) (Point A)
- \((x_2, y_2) = (7, 2)\) (Point B)

Substituting the values into the formula:

\[
d = \sqrt{(7 - (-3))^2 + (2 - 5)^2}
\]
\[
d = \sqrt{(7 + 3)^2 + (2 - 5)^2}
\]
\[
d = \sqrt{(10)^2 + (-3)^2}
\]
\[
d = \sqrt{100 + 9}
\]
\[
d = \sqrt{109}
\]
\[
d \approx 10.4403
\]

Rounding to the nearest tenth, the distance from point A to point B is approximately **10.4 units**.

---

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 of points A and B:

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

Thus, the midpoint of line segment AB is **(2, 3.5)**.