Question

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Find the distance between points M(−1, −10) and P(−12, −3). Round to the nearest tenth.

Answer 1

To find the distance between two points \( M(-1, -10) \) and \( P(-12, -3) \), we can use the distance formula:

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

Here, \( (x_1, y_1) = (-1, -10) \) and \( (x_2, y_2) = (-12, -3) \).

Substitute the coordinates into the formula:

\[
d = \sqrt{((-12) - (-1))^2 + ((-3) - (-10))^2}
\]

Simplify the expressions inside the parentheses:

\[
d = \sqrt{(-12 + 1)^2 + (-3 + 10)^2}
\]

This simplifies to:

\[
d = \sqrt{(-11)^2 + 7^2}
\]

Calculate the squares:

\[
d = \sqrt{121 + 49}
\]

Add the results:

\[
d = \sqrt{170}
\]

Take the square root of 170:

\[
d \approx 13.0
\]

Therefore, the distance between points \( M \) and \( P \) is approximately 13.0 units when rounded to the nearest tenth.