Question

For points P(25, -18) and Q(30, -13), find the distance d(P,Q) and the coordinates of the midpoint M. Options:

A. Distance
B. Midpoint coordinates

Answer 1

The distance between points P(25, -18) and Q(30, -13) is 5√2. The midpoint of these two points is (27.5, -15.5).

Step-by-step explanation:

Given the coordinates of points P(25, -18) and Q(30, -13), we can find the distance and midpoint.

1. Distance: Using the distance formula, d(P,Q) = √((x2 - x1)^2 + (y2 - y1)^2), we can calculate the distance between P and Q as follows:
2. d(P,Q) = √((30 - 25)^2 + (-13 - (-18))^2) = √(5^2 + 5^2) = √(50) = 5√2.
3. Midpoint: The midpoint M can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.
4. x-coordinate of M = (25 + 30) / 2 = 55 / 2 = 27.5
5. y-coordinate of M = (-18 + -13) / 2 = -31 / 2 = -15.5
6. Therefore, the coordinates of the midpoint M are (27.5, -15.5).