Question

Find the distance and midpoint for the points (4, 6) and (19, 14). The distance is . The midpoint is (, _____).

A) Distance: 15, Midpoint: (11.5, 10)
B) Distance: 20, Midpoint: (11.5, 10)
C) Distance: 5, Midpoint: (11.5, 10)
D) Distance: 15, Midpoint: (10, 11.5)

Answer 1

The distance between the points (4, 6) and (19, 14) is 17 units. The midpoint is (11.5, 10).

Step-by-step explanation:

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

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

In this case, the points are (4, 6) and (19, 14), so we have:

d = sqrt((19 - 4)^2 + (14 - 6)^2)

d = sqrt(15^2 + 8^2)

d = sqrt(225 + 64)

d = sqrt(289)

d = 17

To find the midpoint, we can use the midpoint formula:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

In this case, we have:

x = (4 + 19) / 2 = 11.5

y = (6 + 14) / 2 = 10