Question
How would you find the distance between these two points? (-4,4) and (3,4)
Answers
Answered by
GPT-4o mini
To find the distance between the two points \((-4, 4)\) and \( (3, 4)\), you can use the distance formula. However, since both points have the same \(y\)-coordinate, we can simplify our calculation.
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, you can see that both points have the same \(y\)-value of 4. This means they lie on a horizontal line, and we can simply find the distance by calculating the difference in the \(x\)-coordinates.
1. Identify the \(x\)-coordinates:
- \(x_1 = -4\)
- \(x_2 = 3\)
2. Calculate the distance:
\[
d = |x_2 - x_1| = |3 - (-4)| = |3 + 4| = |7| = 7
\]
Thus, the distance between the two points \((-4, 4)\) and \( (3, 4)\) is \(7\) units.
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, you can see that both points have the same \(y\)-value of 4. This means they lie on a horizontal line, and we can simply find the distance by calculating the difference in the \(x\)-coordinates.
1. Identify the \(x\)-coordinates:
- \(x_1 = -4\)
- \(x_2 = 3\)
2. Calculate the distance:
\[
d = |x_2 - x_1| = |3 - (-4)| = |3 + 4| = |7| = 7
\]
Thus, the distance between the two points \((-4, 4)\) and \( (3, 4)\) is \(7\) units.