Question

For the point p(7,-2) and q(12,1), find the distance d(p,q) and the coordinates of the midpoint m of the segment pq.

Answer 1

The distance between the points p(7,-2) and q(12,1) is sqrt(34) and the midpoint of the segment pq is (9.5, -0.5).

Step-by-step explanation:

To find the distance between two points, we can use the distance formula:

d(p,q) = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of point p(7, -2) and q(12, 1) into the formula, we get:

d(p,q) = sqrt((12 - 7)^2 + (1 - (-2))^2) = sqrt(25 + 9) = sqrt(34)

To find the coordinates of the midpoint m, we can use the midpoint formula:

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

Substituting the coordinates of point p(7, -2) and q(12, 1) into the formula, we get:

m = ((7 + 12) / 2, (-2 + 1) / 2) = (9.5, -0.5)