Question

Find the distance between the pair of points. give an exact answer, and, where appropiate, and apporximation to two decimal places. (-6,-1) and (4,3)

Answer 1

• Distance Formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
• Product rule of radicals: √ab = √a x √b

Using our two points, we can solve for the distance as such:

$\sqrt{(4-(-6))^2+(3-(-1))^2}\\ \sqrt{(10)^2+(4)^2}\\ \sqrt{100+16}\\ \sqrt{116}$

Now our exact answer may be √116, however using the product rule of radicals we can further simplify the radical as such:

√116 = √4 x √29 = 2√29.

• Exact Answer: √116 or 2√29
• Approximate Answer: 10.77