Questions: Calculate the distance between the points L=(-2,-2) and F=(-6,3) in the coordinate plane. Give an exact answer (not a decimal approximation). Distance:

Solution Steps

To find the distance between two points in the coordinate plane, we 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. In this case, the points are \(L=(-2,-2)\) and \(F=(-6,3)\).

The coordinates of the two points are given as \( L = (-2, -2) \) and \( F = (-6, 3) \).

To find the distance between the points \( L \) and \( F \), we use the distance formula:

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

Substituting the coordinates of the points into the formula:

\[ \text{Distance} = \sqrt{((-6) - (-2))^2 + (3 - (-2))^2} \]

Calculate the differences and square them:

\[ = \sqrt{(-6 + 2)^2 + (3 + 2)^2} \]

\[ = \sqrt{(-4)^2 + (5)^2} \]

\[ = \sqrt{16 + 25} \]

\[ = \sqrt{41} \]

Final Answer