Question

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

Answer 1

To find the distance of a line defined by two points, you first need to determine the equation of the line. The two points given are \((-10, -10)\) and \((-2, 5)\).

1. **Find the slope (m)** of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the coordinates:

\[
m = \frac{5 - (-10)}{-2 - (-10)} = \frac{15}{8}
\]

2. **Use the point-slope form** of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using one of the points, let’s use \((-10, -10)\):

\[
y - (-10) = \frac{15}{8}(x - (-10))
\]

Simplifying gives:

\[
y + 10 = \frac{15}{8}(x + 10)
\]

3. **Convert to slope-intercept form** (y = mx + b):

Distributing:

\[
y + 10 = \frac{15}{8}x + \frac{150}{8}
\]

Subtracting 10 from both sides:

\[
y = \frac{15}{8}x + \frac{150}{8} - \frac{80}{8}
\]
\[
y = \frac{15}{8}x + \frac{70}{8}
\]

4. **Now, to find the distance between the two points** \((-10, -10)\) and \((-2, 5)\):

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\):

\[
d = \sqrt{((-2) - (-10))^2 + (5 - (-10))^2}
\]
\[
d = \sqrt{(8)^2 + (15)^2}
\]
\[
d = \sqrt{64 + 225}
\]
\[
d = \sqrt{289}
\]
\[
d = 17
\]

Thus, the distance between the two points (and hence the line segment defined by these points) is **17**.