Question

How would you set up the distance formula to find the distance between A and B (1 point) Responses d=(2−−3)2+(−3−4)2−−−−−−−−−−−−−−−−−−√ d is equal to square root of open paren 2 minus negative 3 close paren squared plus open paren negative 3 minus 4 close paren squared end root d=(−4+3)2+(3−−2)2−−−−−−−−−−−−−−−−−−√ d is equal to square root of open paren negative 4 plus 3 close paren squared plus open paren 3 minus negative 2 close paren squared end root d=(−4−3)2+(−3−2)2−−−−−−−−−−−−−−−−−−√ d is equal to square root of open paren negative 4 minus 3 close paren squared plus open paren negative 3 minus 2 close paren squared end root d=(−3−4)2+(2−−3)2−−−−−−−−−−−−−−−−−−√

Answer 1

To set up the distance formula to find the distance between two points, let's denote the points \( A \) and \( B \) with coordinates \( A(x_1, y_1) \) and \( B(x_2, y_2) \). The distance \( d \) between points \( A \) and \( B \) can be calculated using the formula:

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

Now let's clarify which points you're using. If we take \( A = (2, -3) \) and \( B = (-3, 4) \), we can set up the distance formula as follows:

1. Identify the coordinates:
- \( x_1 = 2 \), \( y_1 = -3 \)
- \( x_2 = -3 \), \( y_2 = 4 \)

2. Plug the coordinates into the distance formula:
\[
d = \sqrt{((-3) - 2)^2 + (4 - (-3))^2}
\]

3. Simplify it:
\[
d = \sqrt{(-5)^2 + (7)^2}
\]
\[
d = \sqrt{25 + 49}
\]
\[
d = \sqrt{74}
\]

This method shows how to calculate the distance between two specific points using the distance formula. If you have other points or specific coordinates in mind, please provide those for precise calculations.

Answer 2

A is, (-3,4) and B is, (2,-3)

Answer 3

Thank you for providing the coordinates for points \( A \) and \( B \).

With \( A = (-3, 4) \) and \( B = (2, -3) \), we can set up the distance formula as follows:

1. Identify the coordinates:
- \( x_1 = -3 \), \( y_1 = 4 \)
- \( x_2 = 2 \), \( y_2 = -3 \)

2. Plug the coordinates into the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the values:
\[
d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}
\]

3. Simplify it:
\[
d = \sqrt{(2 + 3)^2 + (-3 - 4)^2}
\]
\[
d = \sqrt{(5)^2 + (-7)^2}
\]
\[
d = \sqrt{25 + 49}
\]
\[
d = \sqrt{74}
\]

Thus, the distance \( d \) between points \( A \) and \( B \) is \( \sqrt{74} \).

Answer 4

Choose the options given for the answer

Answer 5

From your initial message, here are the options you provided, rewritten for clarity:

1. \( d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2} \)
2. \( d = \sqrt{(-4 + 3)^2 + (3 - (-2))^2} \)
3. \( d = \sqrt{(-4 - 3)^2 + (-3 - 2)^2} \)
4. \( d = \sqrt{(-3 - 4)^2 + (2 - (-3))^2} \)

Let's analyze the options based on the coordinates \( A(-3, 4) \) and \( B(2, -3) \):

The correct representation using the distance formula is:

\[
d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}
\]

So option **1** is the correct distance formula setup to find the distance between points \( A \) and \( B \).

Thus, the answer is:
**1.** \( d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2} \)