Question

Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-5, -2) and point (8, -3) rounded to the nearest tenth?
10.3 units

12.6 units

1 unit

13 units

Answer 1

Option D: 13 units is the distance between the two points

Explanation:

Given that the points are $(-5,-2)$ and $(8,-3)$

We need to find the distance between the two points.

The distance between the two points can be determined using the distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let us substitute the points $(-5,-2)$ and $(8,-3)$ in the above formula, we get,

$d=\sqrt{(8-(-5))^2+(-3-(-2))^2}$

Simplifying the terms within the bracket, we have,

$d=\sqrt{(8+5)^2+(-3+2)^2}$

Adding the terms within the bracket, we get,

$d=\sqrt{(13)^2+(-1)^2}$

Squaring the terms, we have,

$d=\sqrt{169+1}$

Adding, we get,

$d=\sqrt{170}$

Simplifying, we have,

$d=13.04$

Rounding off to the nearest tenth, we get,

$d=13.0 \ units$

Hence, the distance between the two points is 13 units.

Therefore, Option D is the correct answer.