Questions: Find the distance between the pair of points (-4,-6) and (5,-5). If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is units. (Simplify your answer. Type an exact answer, using radicals as needed.)

Find the distance between the pair of points (-4,-6) and (5,-5). If necessary, express the answer in simplified radical form and then round to two decimal places.

The distance between the given points is units. (Simplify your answer. Type an exact answer, using radicals as needed.)

Transcript text: Find the distance between the pair of points $(-4,-6)$ and $(5,-5)$. If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is $\square$ units. (Simplify your answer. Type an exact answer, using radicals as needed.)

Solution

Solution Steps

Step 1: Identify the Coordinates

The coordinates of the first point are $(x_1, y_1) = (-4, -6)$ and the second point are $(x_2, y_2) = (5, -5)$.

Step 2: Apply the Distance Formula

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a 2-dimensional Cartesian coordinate system is given by the formula: \[d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\]

Step 3: Substitute the Coordinates into the Formula

Substituting the given coordinates into the formula, we get: \[d = \sqrt{(5 + 4)^2 + (-5 + 6)^2}\]

Step 4: Calculate the Distance

Calculating the distance, we find that $d = 9.06$.