Option D: The distance between the two points is 13 units
Explanation:
It is given that the two points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]
We need to determine the distance between the two points.
It is also given that the distance between the two points can be determined using the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substituting the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] for the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Thus, we get,
[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]
Simplifying, we have,
[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]
Adding the terms, we get,
[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]
Squaring the terms, we have,
[tex]d=\sqrt{169+1}[/tex]
Adding the terms, we get,
[tex]d=\sqrt{170}[/tex]
Simplifying and rounding off the value to the nearest tenth, we have,
[tex]d=13.0 \ units[/tex]
Hence, the distance between the two points is 13 units.
Therefore, Option D is the correct answer.
