What is the distance between
\[(-6, 4)\] and
\[(-8, 6)\]?
Using the distance formula,
\[d = \sqrt{((-6)-(-8))^2 + ((4)-(6))^2} = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \boxed{2\sqrt{2}}.\]
To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is given by:
\[d = \sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2}\]
Let's use this formula to find the distance between \((-6, 4)\) and \((-8, 6)\).
First, identify the values:
\(x_1 = -6\), \(y_1 = 4\)
\(x_2 = -8\), \(y_2 = 6\)
Next, substitute these values into the formula:
\[d = \sqrt{{(-8 - (-6))}^2 + {(6 - 4)}^2}\]
\[d = \sqrt{{(-8 + 6)}^2 + {(6 - 4)}^2}\]
\[d = \sqrt{{-2}^2 + {2}^2}\]
Now, simplify the expression inside the square root:
\[d = \sqrt{4 + 4}\]
\[d = \sqrt{8}\]
Finally, compute the square root to get the final answer:
\[d \approx 2.83\]
Therefore, the distance between \((-6, 4)\) and \((-8, 6)\) is approximately 2.83 units.
To find the distance between two points, we can use the distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
where \((x_1, y_1)\) represents the coordinates of the first point and \((x_2, y_2)\) represents the coordinates of the second point.
In this case, we have:
\((x_1, y_1) = (-6, 4)\) and \((x_2, y_2) = (-8, 6)\).
Let's substitute the values in the formula:
\[d = \sqrt{(-8 - (-6))^2 + (6 - 4)^2}\]
Simplifying this expression gives:
\[d = \sqrt{(-2)^2 + (2)^2}\]
\[d = \sqrt{4 + 4}\]
\[d = \sqrt{8}\]
Therefore, the distance between \((-6, 4)\) and \((-8, 6)\) is \(\sqrt{8}\).
What is the distance between
(-6, 4) and
(-8, 6)?
To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is given by:
\[d = \sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2}\]
Let's use this formula to find the distance between \((-6, 4)\) and \((-8, 6)\).
Using the formula, we have:
\[d = \sqrt{{(-8 - (-6))}^2 + {(6 - 4)}^2}\]
\[d = \sqrt{{(-8 + 6)}^2 + {(6 - 4)}^2}\]
\[d = \sqrt{{(-2)}^2 + {(2)}^2}\]
\[d = \sqrt{{4 + 4}}\]
\[d = \sqrt{8}\]
Therefore, the distance between \((-6, 4)\) and \((-8, 6)\) is \(\sqrt{8}\) or approximately \(\boxed{2.83}\).