Answer:
A)
[tex]\sqrt{290}\approx 17.0\text{ units}[/tex]
B)
[tex]\sqrt{53}\approx7.3\text{ units}[/tex]
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Problem 1)
We have the two points (-4, 5) and (7, 18).
Let (-4, 5) be (x₁, y₁) and let (7, 18) be (x₂, y₂).
Substitute:
[tex]d=\sqrt{(7-(-4))^2+(18-5)^2}[/tex]
Evaluate:
[tex]\begin{aligned}d&=\sqrt{(11)^2+(13)^2}\\&=\sqrt{121+169}\\&=\sqrt{290}\approx17.0\end{aligned}[/tex]
Problem 2)
We have the two points (-2, -3) and (-4, 4).
Similarly, we will let (-2, -3) be (x₁, y₁) and (-4, 4) be (x₂, y₂).
Substitute:
[tex]d=\sqrt{(-4-(-2))^2+(4-(-3))^2[/tex]
Evaluate:
[tex]\begin{aligned}d&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\approx7.3\end{aligned}[/tex]
