To calculate the distance between points D (-5, -5) and E (3, 5), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1)\) are the coordinates of point D and \((x_2, y_2)\) are the coordinates of point E.
Substituting the values, we have:
\[ x_1 = -5, \quad y_1 = -5, \quad x_2 = 3, \quad y_2 = 5 \]
Now, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\[ x_2 - x_1 = 3 - (-5) = 3 + 5 = 8 \] \[ y_2 - y_1 = 5 - (-5) = 5 + 5 = 10 \]
Now plug these into the distance formula:
\[ d = \sqrt{(8)^2 + (10)^2} \] \[ d = \sqrt{64 + 100} \] \[ d = \sqrt{164} \]
Now, we can simplify \(\sqrt{164}\):
\[ \sqrt{164} \approx 12.81 \text{ (when calculated)} \]
To find an approximate numerical value, we can round this:
Thus, the distance between points D and E is approximately 12.81 units.