Find the distance between the points $$ (-3,-4) $$ and $$ (5,-4) $$. Distance: $$ \square $$

Question

UpStudy AI · Accepted Answer

**Step 1: Write down the distance formula**

The distance $$ d $$ between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by

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

**Step 2: Substitute the given coordinates**

For the points $$(-3, -4)$$ and $$(5, -4)$$:

$$
x_1 = -3, \quad y_1 = -4, \quad x_2 = 5, \quad y_2 = -4
$$

Substitute these values into the formula:

$$
d = \sqrt{(5 - (-3))^2 + (-4 - (-4))^2}
$$

**Step 3: Simplify the expression**

Calculate the differences:

$$
5 - (-3) = 5 + 3 = 8
$$
$$
-4 - (-4) = -4 + 4 = 0
$$

Then the distance becomes:

$$
d = \sqrt{8^2 + 0^2} = \sqrt{64 + 0} = \sqrt{64}
$$

**Step 4: Compute the distance**

$$
d = 8
$$

Distance: $$ \boxed{8} $$
The distance between the points $$(-3, -4)$$ and $$(5, -4)$$ is $$8$$.

Find the distance between the points \( (-3,-4) \) and \( (5,-4) \). Distance: \( \square \)