Question

what is the distance from point A(-3,5) to point B(7,3)? Round to the nearest tenth. and what is the midpoint of the line segment AB

Answer 1

To find the distance between points A(-3, 5) and B(7, 3), 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 in the values from points A and B:

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

Now, we can calculate the distance \( d \):

\[
d = \sqrt{(7 - (-3))^2 + (3 - 5)^2}
\]
\[
= \sqrt{(7 + 3)^2 + (3 - 5)^2}
\]
\[
= \sqrt{(10)^2 + (-2)^2}
\]
\[
= \sqrt{100 + 4}
\]
\[
= \sqrt{104}
\]
\[
\approx 10.2 \quad (\text{rounded to the nearest tenth})
\]

Now, to find the midpoint \( M \) of the line segment AB, we use the midpoint formula:

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

Substituting in the coordinates:

\[
M = \left( \frac{-3 + 7}{2}, \frac{5 + 3}{2} \right)
\]
\[
= \left( \frac{4}{2}, \frac{8}{2} \right)
\]
\[
= (2, 4)
\]

Thus, the distance from point A to point B is approximately **10.2**, and the midpoint of the line segment AB is **(2, 4)**.