Questions: (5,6) and (12,12)

Solution Steps

We are given two points in the Cartesian plane: \( (x_1, y_1) = (5, 6) \) and \( (x_2, y_2) = (12, 12) \).

To find the distance \( d \) between the two points, we use the distance formula:

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

Substituting the coordinates into the formula, we have:

\[ d = \sqrt{(12 - 5)^2 + (12 - 6)^2} \]

Calculating the differences:

\[ d = \sqrt{(7)^2 + (6)^2} \]

Now, we compute the squares:

\[ d = \sqrt{49 + 36} \]

Adding the squares gives:

\[ d = \sqrt{85} \]

Thus, the distance between the points \( (5, 6) \) and \( (12, 12) \) is \( \sqrt{85} \).

Final Answer