Problem 12 - College Algebra

Question

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (0,-\sqrt{3}) \text { and }(\sqrt{5}, 0) $$

Step-by-Step Solution

Answer

The distance between the given points is approximately 2.83 when rounded to two decimal places.

Step 1: Identifying the coordinates

Firstly, identify the coordinates of the two points: point A is (0, -√3), so \(x_1 = 0\) and \(y_1 = -\sqrt{3} \). Point B is (√5, 0), so \(x_2 = \sqrt{5} \) and \(y_2 = 0 \)

Step 2: Applying the distance formula

Plug these coordinates into the distance formula \(d = \sqrt{(x_2 - x_1 )^2 + (y_2 - y_1)^2}\). After inserting the values, get \[d = \sqrt{(\sqrt{5} - 0 )^2 + (0 - - \sqrt{3})^2 }\]

Step 3: Simplifying the expression

After simplifying the above expression, you get \(d = \sqrt{5 + 3 }\) which simplifies to \(d = \sqrt{8}\)

Step 4: Rounding to two decimal places

When you calculate the approximate value for \(\sqrt{8}\), you'll find it's approximately equal to 2.83 when rounded to two decimal places