Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and

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Question: Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)

Options:

Correct Answer: (3, 4, 5)

Solution:

Midpoint M = ((2+4)/2, (3+5)/2, (4+6)/2) = (3, 4, 5).

Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)

Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)

Step 1: Identify the coordinates of point A, which are (2, 3, 4).
Step 2: Identify the coordinates of point B, which are (4, 5, 6).
Step 3: To find the midpoint, use the formula: Midpoint M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2).
Step 4: Substitute the coordinates of A and B into the formula: M = ((2 + 4)/2, (3 + 5)/2, (4 + 6)/2).
Step 5: Calculate the x-coordinate: (2 + 4)/2 = 6/2 = 3.
Step 6: Calculate the y-coordinate: (3 + 5)/2 = 8/2 = 4.
Step 7: Calculate the z-coordinate: (4 + 6)/2 = 10/2 = 5.
Step 8: Combine the results to get the midpoint M = (3, 4, 5).

Midpoint Formula – The midpoint of a line segment in 3D space is calculated by averaging the coordinates of the endpoints.