Question

How would you set up the distance formula to find the distance between a and b?
(The coordinates for the line segment are ( A (-3,4) and B(2,-3))

Answer 1

To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), you can use the distance formula:

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

In your case, the coordinates for the points are:
- \( A(-3, 4) \) with \( x_1 = -3 \) and \( y_1 = 4 \)
- \( B(2, -3) \) with \( x_2 = 2 \) and \( y_2 = -3 \)

Now, plug in the values into the distance formula:

1. Calculate \( x_2 - x_1 \):
\[
x_2 - x_1 = 2 - (-3) = 2 + 3 = 5
\]

2. Calculate \( y_2 - y_1 \):
\[
y_2 - y_1 = -3 - 4 = -7
\]

3. Substitute these results into the distance formula:
\[
d = \sqrt{(5)^2 + (-7)^2}
\]
\[
= \sqrt{25 + 49}
\]
\[
= \sqrt{74}
\]

Thus, the distance between points \( A \) and \( B \) is \( \sqrt{74} \). If you need the numerical approximation, it is approximately \( 8.60 \).