Distance Between Two Points

Question

A) Find the distance, to the nearest hundredth, between the given points.
P1(4, −1) and P2(−3, −2)



B) Find the coordinates of the midpoint of the line segment connecting the points.
(x, y) =

Answer 1

Jane,

 

(a) Use the distance formula to calculate the distance between the two points.

 

d = sqrt[(x₂ - x1)² + (y₂ - y₁)²]

 

d = sqrt[(-3 - 4)² + (-2 - (-1))²]

 

d = sqrt[(-7)² + (-1)²)]

 

d = sqrt[49 + 1]

 

d = sqrt(50) = sqrt(25 * 2) = 5√2 = 7.07 (distance between the points)

 

The midpoint of the segment is:

 

m = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

 

m = [(4 + (-3))/2 , (-1 + (-2))/2]

 

m = [1/2, -3/2] (midpoint of the segment that connects the two points.

 

Hope this helps!