Question

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

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 answer your questions, we will use the distance formula and the midpoint formula.

### Question 1
**Distance formula:**
The distance \( d \) between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

For points \( A(-3, 5) \) and \( B(7, 2) \):
- \( x_1 = -3 \)
- \( y_1 = 5 \)
- \( x_2 = 7 \)
- \( y_2 = 2 \)

Now, plug in the values into the formula:
\[
d = \sqrt{(7 - (-3))^2 + (2 - 5)^2}
\]
\[
= \sqrt{(7 + 3)^2 + (2 - 5)^2}
\]
\[
= \sqrt{(10)^2 + (-3)^2}
\]
\[
= \sqrt{100 + 9}
\]
\[
= \sqrt{109}
\]
Calculating \( \sqrt{109} \):
\[
\sqrt{109} \approx 10.4403
\]
Rounding to the nearest tenth, the distance is approximately:
\[
\text{Distance} \approx 10.4 \text{ units}
\]

### Question 2
**Midpoint formula:**
The midpoint \( M \) of a line segment between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

For points \( A(-3, 5) \) and \( B(7, 2) \):
\[
M = \left( \frac{-3 + 7}{2}, \frac{5 + 2}{2} \right)
\]
\[
= \left( \frac{4}{2}, \frac{7}{2} \right)
\]
\[
= (2, 3.5)
\]

### Final Answers
1. The distance from point A to point B is approximately **10.4 units**.
2. The midpoint of line segment AB is **(2, 3.5)**.