To find the distance between the two points [tex]\((-5, -3)\)[/tex] and [tex]\((-8, -7)\)[/tex], let's break it down step-by-step:
1. Identify and plot the given points:
- The first point is [tex]\((-5, -3)\)[/tex].
- The second point is [tex]\((-8, -7)\)[/tex].
2. Calculate the differences in the coordinates:
- The change in [tex]\(x\)[/tex] coordinates ([tex]\(\Delta x\)[/tex]) is:
[tex]\[
x_2 - x_1 = -8 - (-5) = -8 + 5 = -3
\][/tex]
- The change in [tex]\(y\)[/tex] coordinates ([tex]\(\Delta y\)[/tex]) is:
[tex]\[
y_2 - y_1 = -7 - (-3) = -7 + 3 = -4
\][/tex]
3. Interpret these differences as the sides of a right triangle:
- You now have a right triangle with side lengths of [tex]\(|\Delta x| = 3\)[/tex] units and [tex]\(|\Delta y| = 4\)[/tex] units.
4. Apply the Pythagorean Theorem to find the hypotenuse, which represents the distance between the two points:
[tex]\[
\text{Distance} = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0
\][/tex]
5. Round the distance if necessary:
- In this case, the distance comes out to be exactly 5.0, so no rounding is necessary.
Therefore, the distance between the points [tex]\((-5, -3)\)[/tex] and [tex]\((-8, -7)\)[/tex] is 5.0 units.
