Easy Algebra Step-by-Step

The Cartesian Coordinate Plane 177

Step 2. Evaluate the formula for the values from step 1.

d =^2

2

()xx 21 x +()yyy −y 1 =

22

() 5 () 1 +()()− 33 44

= () 5122 +()− 3434 = () (^622) () 77 = 36 + 49 = 85
Step 3. State the distance.
The distance between (−1, 4) and (5, −3) is 85 units.

Finding the Midpoint Between Two Points in the Plane

You can find the midpoint between two points using the following

formula.

Midpoint Between Two Points

The midpoint between two points (x 1 , y 1 ) and

(x 2 , y 2 ) in a coordinate plane is the point with

coordinates

x 12 x yy 12 y

22

⎛ ++xx 2 y

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

,

Problem Find the midpoint between (−1, 4) and (5, −3).

Solution

Step 1. Specify (x 1 , y 1 ) and (x 2 , y 2 ) and identify values for x 1 , y 1 , x 2 , and y 2.

Let (x 1 , y 1 ) = (−1, 4) and (x 2 , y 2 ) = (5, −3). Then x 1 = −1, y 1 = 4, x 2 = 5,

and y 2 = −3.

Step 2. Evaluate the formula for the values from step 1.

Midpoint =

xx 12 x yyy 2

22

⎛ + +

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

, =

⎛−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

15 + ⎞⎞⎞⎞

2

43 −

2

, =

4

2

1

2

⎛ ,

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ = 21

2

⎛ ,

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞

Step 3. State the midpoint.

The midpoint between (−1, 4) and (5, −3) is 2

1

2

⎛ ,

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞.

P When you use the midpoint

formula, be sure to put plus signs,

not minus signs, between the two

x values and the two y values.