Answer:
[tex]d=\sqrt{149}\approx12.21[/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]
We have the two points (-1, 7) and (-8, -3).
Let (-1, 7) be (x₁, y₁) and let (-8, -3) be (x₂, y₂). Substitute:
[tex]d=\sqrt{(-8-(-1))^2+(-3-7)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(-8+1)^2+(-10)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(-7)^2+(-10)^2}[/tex]
Square:
[tex]d=\sqrt{49+100}[/tex]
Add:
[tex]d=\sqrt{149}\approx12.21[/tex]
This cannot be simplified. Hence, the distance between (-1, 7) and (-8, -3) is √(149) or approximately 12.21 units.
