Questions: Find the distance between the points whose coordinates are given. [ (-4,-20),(-6,6) ]

Solution Steps

To find the distance between two points in a 2D plane, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

1. Identify the coordinates of the two points.
2. Substitute these coordinates into the distance formula.
3. Calculate the result using Python.

The coordinates of the two points are given as: \[ (x_1, y_1) = (-4, -20) \quad \text{and} \quad (x_2, y_2) = (-6, 6) \]

Using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] we substitute the coordinates: \[ \text{Distance} = \sqrt{((-6) - (-4))^2 + (6 - (-20))^2} \]

Calculating the differences: \[ x_2 - x_1 = -6 + 4 = -2 \quad \text{and} \quad y_2 - y_1 = 6 + 20 = 26 \] Now substituting these values back into the formula: \[ \text{Distance} = \sqrt{(-2)^2 + (26)^2} = \sqrt{4 + 676} = \sqrt{680} \]

Calculating the square root: \[ \sqrt{680} \approx 26.0768 \]

Final Answer