Option D: 13 units is the distance between the two points
Explanation:
Given that the points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]
We need to find the distance between the two points.
The distance between the two points can be determined using the distance formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let us substitute the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] in the above formula, we get,
[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]
Simplifying the terms within the bracket, we have,
[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]
Adding the terms within the bracket, we get,
[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]
Squaring the terms, we have,
[tex]d=\sqrt{169+1}[/tex]
Adding, we get,
[tex]d=\sqrt{170}[/tex]
Simplifying, we have,
[tex]d=13.04[/tex]
Rounding off to the nearest tenth, we get,
[tex]d=13.0 \ units[/tex]
Hence, the distance between the two points is 13 units.
Therefore, Option D is the correct answer.
