Find the distance between the points. Give an exact
answer and an approximation to three decimal places.
and

Ask by Lambert Ruiz. in the United States

Jan 21,2025

Question

Find the distance between the points. Give an exact answer and an approximation to three decimal places. $$ (-1,-6) $$ and $$ (-11,-11) $$

UpStudy AI · Accepted Answer

To find the distance between the points $$(-1, -6)$$ and $$(-11, -11)$$, we can use the distance formula:

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

Plugging in the given coordinates:

$$
x_1 = -1, \quad y_1 = -6, \quad x_2 = -11, \quad y_2 = -11
$$

Calculate the differences:

$$
x_2 - x_1 = -11 - (-1) = -10
$$
$$
y_2 - y_1 = -11 - (-6) = -5
$$

Now, substitute these into the distance formula:

$$
\text{Distance} = \sqrt{(-10)^2 + (-5)^2} = \sqrt{100 + 25} = \sqrt{125}
$$

**Exact Answer:**
$$
5\sqrt{5} \text{ units}
$$

**Approximation to Three Decimal Places:**

$$
5\sqrt{5} \approx 5 \times 2.236 = 11.180 \text{ units}
$$

**Final Answer:**

The distance is exactly $$5\sqrt{5}$$ units and approximately 11.180 units.
The distance between the points $$(-1, -6)$$ and $$(-11, -11)$$ is exactly $$5\sqrt{5}$$ units, which is approximately 11.180 units.

Find the distance between the points. Give an exact
answer and an approximation to three decimal places.
and

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