Question

Find the distance between the two points rounding to the nearest tenth (if necessary).
(3,−4) and (9,−9)

Answer 1

To find the distance between the two points \((3, -4)\) and \((9, -9)\), we can use the distance formula:

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

Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Here, we have:

- \(x_1 = 3\)
- \(y_1 = -4\)
- \(x_2 = 9\)
- \(y_2 = -9\)

Now, substitute the values into the formula:

\[
d = \sqrt{(9 - 3)^2 + (-9 - (-4))^2}
\]

Calculating the differences:

\[
d = \sqrt{(6)^2 + (-9 + 4)^2}
\]

This simplifies to:

\[
d = \sqrt{(6)^2 + (-5)^2}
\]

Now calculate the squares:

\[
d = \sqrt{36 + 25}
\]

Adding the two values:

\[
d = \sqrt{61}
\]

Now we can find the numerical value:

\[
d \approx 7.8102
\]

Rounding to the nearest tenth, we find:

\[
d \approx 7.8
\]

Thus, the distance between the two points is approximately **7.8** units.