Question

For the points P(-20, -5) and Q(-13, 0), find the distance d(P, Q) and the coordinates of the midpoint M of the segment PQ.

Answer 1

The distance between points P and Q is the square root of 74, and the coordinates of the midpoint M are (-16.5, -2.5). The formulas for distance and midpoint are applied to the given coordinates to find these results.

Step-by-step explanation:

To find the distance between two points P and Q in the Cartesian plane, we can use the distance formula which is derived from the Pythagorean theorem:

d(P, Q) = √[(x2 - x1)² + (y2 - y1)²]

For points P(-20, -5) and Q(-13, 0), the distance is:

d(P, Q) = √[(-13 - (-20))² + (0 - (-5))²] = √[(7)² + (5)²] = √[49 + 25] = √[74]

To find the coordinates of the midpoint M of the segment PQ, we use the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

So the midpoint M is:

M = ((-20 - 13)/2, (-5 + 0)/2) = (-33/2, -5/2) = (-16.5, -2.5)