Midpoint of (1, 5) and (3, 1)

Find the midpoint of the line segment from (1, 5) to (3, 1).

Answer: =

Step-by-Step Solution

Step 1 Midpoint Formula

The midpoint M between two points P₁(x₁,y₁) and P₂(x₂,y₂) is:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The midpoint is the average of the coordinates

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Step 2 Identify the Points

Point 1: P₁(1, 5)

Point 2: P₂(3, 1)

P₁(1, 5), P₂(3, 1)

Step 3 Calculate x-coordinate of Midpoint

x_M = (x₁ + x₂)/2

x_M = (1 + 3)/2

x_M = 4/2

x_M = 2

Step 4 Calculate y-coordinate of Midpoint

y_M = (y₁ + y₂)/2

y_M = (5 + 1)/2

y_M = 6/2

y_M = 3

Step 5 Midpoint Result

M = (2, 3)

Step 6 Verification

Distance from P₁ to M should equal distance from M to P₂

M is equidistant from both endpoints

Midpoint divides segment in ratio 1:1

Step 7 Geometric Interpretation

The midpoint M lies exactly halfway between P₁ and P₂

If you draw the line segment from P₁ to P₂, M is at its center

M divides the segment into two equal parts

Center of line segment