To find the length between the points \((-1, 6)\) and \( (5, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For the points \((-1, 6)\) and \((5, -2)\), we have:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 5\)
- \(y_2 = -2\)
Now, plug in the values:
\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \] \[ d = \sqrt{(5 + 1)^2 + (-8)^2} \] \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]
So the distance between the points is \(10\).
The answer is 10.
1 answer