Question

question 2
find the distance between each pair of points.
(-9,-9) and (-4,2) ab = \sqrt{(-4 - (-9))^{2}+(2 - (-9))^{2}}

Explanation:

Step1: Simplify the expressions inside the square - root

First, simplify \(-4-(-9)\) and \(2 - (-9)\).
\(-4-(-9)=-4 + 9=5\) and \(2-(-9)=2 + 9 = 11\).
The distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \((x_1,y_1)=(-9,-9)\) and \((x_2,y_2)=(-4,2)\) becomes \(d=\sqrt{5^2+11^2}\).

Step2: Calculate the squares and the sum

Calculate \(5^2 = 25\) and \(11^2=121\). Then \(5^2+11^2=25 + 121=146\). So \(d=\sqrt{146}\).

Answer:

\(\sqrt{146}\)