Question

Question 8 of 20 (1 point) | Attempt 3 of Unlimited View question in a popup For the points (V2.-13) and (-4/2,3/3). (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points

a) Distance: 4 units; Midpoint: (-1, 5)
b) Distance: 5 units; Midpoint: (-2, 3.5)
c) Distance: 5 units; Midpoint: (-1, 5)
d) Distance: 4 units; Midpoint: (-2, 3.5)

Answer 1

To find the distance between two points, we use the distance formula and to find the midpoint of a line segment, we use the midpoint formula. The correct answer is b) Distance: 5 units; Midpoint: (-2, 3.5).

Step-by-step explanation:

(a) To find the distance between two points, we use the distance formula, which is based on the Pythagorean theorem. Let's call the coordinates of the first point (x1, y1) and the coordinates of the second point (x2, y2).

The distance between the points is given by the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). Substituting the given coordinates, we have d = sqrt((-4/2 - 2)^2 + (3/3 - (-13))^2).

(b) The midpoint of a line segment is simply the average of the x-coordinates and the average of the y-coordinates of the two endpoints.

Let's call the coordinates of the first endpoint (x1, y1) and the coordinates of the second endpoint (x2, y2). The midpoint is given by the formula: ((x1 + x2)/2, (y1 + y2)/2). Substituting the given coordinates, we have the midpoint as ((-4/2 + 2)/2, (3/3 + (-13))/2).