Question
How would you set up the distance formula to find the distance between points E and F
Answers
GPT-4o mini
To find the distance between two points, E and F, in a Cartesian coordinate system, you can use the distance formula. The distance formula is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where:
- \( d \) is the distance between the points.
- \((x_1, y_1)\) are the coordinates of point E.
- \((x_2, y_2)\) are the coordinates of point F.
To set it up, follow these steps:
1. Identify the coordinates of points E and F. Let's say:
- Point E has coordinates \((x_1, y_1)\)
- Point F has coordinates \((x_2, y_2)\)
2. Substitute the coordinates into the distance formula.
For example, if the coordinates of E are (2, 3) and the coordinates of F are (5, 7), you would set it up as follows:
\[
d = \sqrt{(5 - 2)^2 + (7 - 3)^2}
\]
3. Simplify the expressions inside the square root:
\[
d = \sqrt{(3)^2 + (4)^2}
\]
4. Calculate the squares and then find the square root:
\[
d = \sqrt{9 + 16} = \sqrt{25} = 5
\]
So, the distance between points E and F is 5 units. You can replace the coordinates with the actual values for points E and F to find the specific distance you need.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where:
- \( d \) is the distance between the points.
- \((x_1, y_1)\) are the coordinates of point E.
- \((x_2, y_2)\) are the coordinates of point F.
To set it up, follow these steps:
1. Identify the coordinates of points E and F. Let's say:
- Point E has coordinates \((x_1, y_1)\)
- Point F has coordinates \((x_2, y_2)\)
2. Substitute the coordinates into the distance formula.
For example, if the coordinates of E are (2, 3) and the coordinates of F are (5, 7), you would set it up as follows:
\[
d = \sqrt{(5 - 2)^2 + (7 - 3)^2}
\]
3. Simplify the expressions inside the square root:
\[
d = \sqrt{(3)^2 + (4)^2}
\]
4. Calculate the squares and then find the square root:
\[
d = \sqrt{9 + 16} = \sqrt{25} = 5
\]
So, the distance between points E and F is 5 units. You can replace the coordinates with the actual values for points E and F to find the specific distance you need.