For the points (-8, -1) and (2, -5),

(a) Find the exact distance between the points.
(b) Find the midpoint of the line segment whose endpoints are the given points.

1 answer

To find the distance between the points \((-8, -1)\) and \( (2, -5)\), we can use the distance formula:

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

Here, we have:

  • \( (x_1, y_1) = (-8, -1) \)
  • \( (x_2, y_2) = (2, -5) \)

Substituting in the coordinates into the formula:

\[ d = \sqrt{(2 - (-8))^2 + (-5 - (-1))^2} \] \[ d = \sqrt{(2 + 8)^2 + (-5 + 1)^2} \] \[ d = \sqrt{(10)^2 + (-4)^2} \] \[ d = \sqrt{100 + 16} \] \[ d = \sqrt{116} \] \[ d = \sqrt{4 \cdot 29} \] \[ d = 2\sqrt{29} \]

So the exact distance between the points is \( \boxed{2\sqrt{29}} \).


Next, to find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:

\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Using the coordinates from above:

\[ \text{Midpoint} = \left( \frac{-8 + 2}{2}, \frac{-1 + (-5)}{2} \right) \]

Calculating the x-coordinate:

\[ \frac{-8 + 2}{2} = \frac{-6}{2} = -3 \]

Calculating the y-coordinate:

\[ \frac{-1 - 5}{2} = \frac{-6}{2} = -3 \]

Thus, the midpoint is:

\[ \text{Midpoint} = (-3, -3) \]

So the midpoint of the line segment is \( \boxed{(-3, -3)} \).

Similar Questions
    1. answers icon 1 answer
  1. For the points (6, - 1) and (8, - 9),(a) Find the exact distance between the points. (b) Find the midpoint of the line segment
    1. answers icon 1 answer
    1. answers icon 2 answers
  2. Consider the points (3, –1) and(9, 2). (a) State the midpoint of the line segment with the given endpoints. (b) Find the
    1. answers icon 7 answers
more similar questions