Question

Find the distance of Line B Your answer should be an integer.
the point of the line is (-9,-10) and (-2,5)

Answer 1

To find the distance (length) of the line segment defined by the points \((-9, -10)\) and \((-2, 5)\), we can use the distance formula, which is given by:

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

In this case, the coordinates of the two points are:
- \((x_1, y_1) = (-9, -10)\)
- \((x_2, y_2) = (-2, 5)\)

Now, substituting the values into the distance formula:

\[
d = \sqrt{((-2) - (-9))^2 + (5 - (-10))^2}
\]

Calculating the differences:

\[
d = \sqrt{(-2 + 9)^2 + (5 + 10)^2}
\]
\[
d = \sqrt{(7)^2 + (15)^2}
\]
\[
d = \sqrt{49 + 225}
\]
\[
d = \sqrt{274}
\]

Now we simplify \(\sqrt{274}\):

Finding the square root of 274, we see that it is not a perfect square, but we can approximate it or find its integer part. However, as requested, we need the distance in its integer form.

Calculating \(\sqrt{274}\) gives approximately:

\[
\sqrt{274} \approx 16.52
\]

Rounding down to the nearest integer gives:

\[
\text{Distance} = 16
\]

Thus, the distance of the line segment is:

\[
\boxed{16}
\]