Midpoint of (2, 3) and (5, 9)

Find the midpoint of the line segment from (2, 3) to (5, 9).

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(2, 3)

Point 2: P₂(5, 9)

P₁(2, 3), P₂(5, 9)

Step 3 Calculate x-coordinate of Midpoint

x_M = (x₁ + x₂)/2

x_M = (2 + 5)/2

x_M = 7/2

Step 4 Calculate y-coordinate of Midpoint

y_M = (y₁ + y₂)/2

y_M = (3 + 9)/2

y_M = 12/2

y_M = 6

Step 5 Midpoint Result

M = (7/2, 6)

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