Question

What are the lengths of each segment? Thank you!

Answer 1

`\displaystyle a=√(17)\text{ units} \text{ and } b=3√(2)\text{ units}`

Explanation:

To determine the distance between any two points, we can use the distance formula. The distance formula is given by:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

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:

`\begin{aligned} a&=√((-1-(-2))^2+(-1-3)^2)\\\\&=√((1)^2+(-4)^2)\\\\&=√(1+16)=√(17)\text{ units} \end{aligned}`

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:

`\displaystyle \begin{aligned} b&=√((-1-2)^2+(-1-2)^2)\\\\&=√((-3)^2+(-3)^2)\\\\&=√(9+9)=√(18)=√(3^2\cdot 2)=3√(2)\text{ units}\end{aligned}`