To find the distance between the two points \((-4, 5)\) and \((0, -6)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (-4, 5)\) and \((x_2, y_2) = (0, -6)\).
Now, substitute the coordinates into the formula:
\[ d = \sqrt{(0 - (-4))^2 + (-6 - 5)^2} \]
This simplifies to:
\[ d = \sqrt{(0 + 4)^2 + (-6 - 5)^2} \] \[ d = \sqrt{(4)^2 + (-11)^2} \] \[ d = \sqrt{16 + 121} \] \[ d = \sqrt{137} \]
Thus, the distance between the points \((-4, 5)\) and \((0, -6)\) is \(\sqrt{137}\).
1 answer