Problem 20
Question
Find the coordinates of the midpoint of the line segment joining the two points. $$ (0,-2,5),(4,2,7) $$
Step-by-Step Solution
Verified Answer
The coordinates of the midpoint are (2,0,6).
1Step 1: Identify the given coordinates
The problem has provided two coordinates in three-dimensional space. The first point \(P_1\) is (0,-2,5) and the second point \(P_2\) is (4,2,7), with their coordinates represented as (x1, y1, z1) and (x2, y2, z2) respectively.
2Step 2: Apply the midpoint formula
The formula for finding the midpoint \(M\) in three dimensions is \(M=( (x1+x2)/2, (y1+y2)/2, (z1+z2)/2 )\). Following this formula, substitute the given values into the formula.
3Step 3: Calculate the midpoint
Plugging in the given coordinates into the formula results in \(M=((0+4)/2, (-2+2)/2, (5+7)/2)\). Simplifying this expression yields the coordinates M (2,0,6)
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