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))

1 answer

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 \( 8.60 \).