Question
How would you setup the distance formula to find the distance between A and B. A(-3,4) B(2,-3)
Answers
GPT-4o mini
To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in a Cartesian coordinate system, you can use the distance formula given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the coordinates of point \( A \) are \( (-3, 4) \) and for point \( B \) they are \( (2, -3) \). Let's assign the coordinates:
- \( x_1 = -3 \)
- \( y_1 = 4 \)
- \( x_2 = 2 \)
- \( y_2 = -3 \)
Now plug these values into the distance formula:
\[
d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}
\]
Calculating the differences:
\[
d = \sqrt{(2 + 3)^2 + (-3 - 4)^2}
\]
This simplifies to:
\[
d = \sqrt{(5)^2 + (-7)^2}
\]
Now, calculate the squares:
\[
d = \sqrt{25 + 49}
\]
Adding the squared values gives:
\[
d = \sqrt{74}
\]
Therefore, the distance between points \( A \) and \( B \) is:
\[
d = \sqrt{74}
\]
If you want to express it in decimal form, you can approximate \( \sqrt{74} \) as approximately \( 8.6 \).
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the coordinates of point \( A \) are \( (-3, 4) \) and for point \( B \) they are \( (2, -3) \). Let's assign the coordinates:
- \( x_1 = -3 \)
- \( y_1 = 4 \)
- \( x_2 = 2 \)
- \( y_2 = -3 \)
Now plug these values into the distance formula:
\[
d = \sqrt{(2 - (-3))^2 + (-3 - 4)^2}
\]
Calculating the differences:
\[
d = \sqrt{(2 + 3)^2 + (-3 - 4)^2}
\]
This simplifies to:
\[
d = \sqrt{(5)^2 + (-7)^2}
\]
Now, calculate the squares:
\[
d = \sqrt{25 + 49}
\]
Adding the squared values gives:
\[
d = \sqrt{74}
\]
Therefore, the distance between points \( A \) and \( B \) is:
\[
d = \sqrt{74}
\]
If you want to express it in decimal form, you can approximate \( \sqrt{74} \) as approximately \( 8.6 \).