(1) The distance between two points (x1,y1) and (x2,y2) is calculated using the formula: distance = √(x2 - x1)2 + (y2 - y1)2. (2) The midpoint between points A(x1,y1) and B(x2,y2) is calculated as M(x,y) = (x1 + x2/2, y1 + y2/2). (3) For example, the distance between points (-1,3) and (2,-6) is 9.49 units.

1. Accelerated Math 2
•Distance between 2 points
•Mid-point of 2 points

2. Distance between two points.
y Using Pythagoras’ Theorem,
B(18,17) AB2 = (18 - 5)2 + (17 - 3)2
17
AB2 = 132 + 142
17 – 3 = 14 units
3 A(5,3)
18 – 5 = 13 units
x
5 18

3. Distance between two points.
In general,
y
B(x2,y2) AB2 = (y2-y1)2 + (x2-x1)2
y2
Hence, the formula for
Length of AB or Distance
Length = y2 – y1
between A and B is
y1 A(x1,y1)
Length = x2 – x1
x
x1 x2

4. Find the distance between the points (-1,3)
and (2,-6)
• Simply by using the formula:
(-1,3) and (2,-6)
(x1,y1) and (x2,y2)
Since
= 9.49 units (3 sig. fig)

5. The mid-point of two points.
Look at it’s horizontal length
y
18 + 5
Mx =
Mid-point of AB
2
B(18,17)
17
= 11.5
(11.5, 10) Look at it’s vertical length
10
17 + 3
My =
2
3 A(5,3)
= 10
11.5
x
5 18

6. The mid-point of two points.
Look at it’s horizontal length
y
x1 + x2
Mx =
2
B(18,17)
y2
Mid-point of AB
Look at it’s vertical length
y1 + y2
My =
2
Formula for mid-point is
y1 A(5,3) x1 + x2 y1 + y2
M AB = ( , )
x 2 2
x1 x2