Answer:
[tex]\displaystyle a=\sqrt{17}\text{ units} \text{ and } b=3\sqrt{2}\text{ units}[/tex]
Step-by-step explanation:
To determine the distance between any two points, we can use the distance formula. The distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
a is the distance between the points (-2, 3) and (-1, -1). Let (-2, 3) be (x₁, y₁) and let (-1, -1) be (x₂, y₂). Substitute and evaluate:
[tex]\begin{aligned} a&=\sqrt{(-1-(-2))^2+(-1-3)^2}\\\\&=\sqrt{(1)^2+(-4)^2}\\\\&=\sqrt{1+16}=\sqrt{17}\text{ units} \end{aligned}[/tex]
b is the distance between the points (2, 2) and (-1, -1). Again, we can let (2, 2) be (x₁, y₁) and (-1, -1) be (x₂, y₂). Substitute and evaluate:
[tex]\displaystyle \begin{aligned} b&=\sqrt{(-1-2)^2+(-1-2)^2}\\\\&=\sqrt{(-3)^2+(-3)^2}\\\\&=\sqrt{9+9}=\sqrt{18}=\sqrt{3^2\cdot 2}=3\sqrt{2}\text{ units}\end{aligned}[/tex]
