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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, the coordinates are:
- \( (x_1, y_1) = (-1, 6) \)
- \( (x_2, y_2) = (5, -2) \)
Now, let's plug in the values:
-
Calculate \(x_2 - x_1\): \[ x_2 - x_1 = 5 - (-1) = 5 + 1 = 6 \]
-
Calculate \(y_2 - y_1\): \[ y_2 - y_1 = -2 - 6 = -8 \]
-
Now, substitute these into the distance formula: \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \] \[ d = 10 \]
Thus, the distance between the points \((-1, 6)\) and \((5, -2)\) is \(10\).
The answer is \(10\).
1 answer