Question 1

What is the midpoint formula?

Accepted Answer

M = ((x₁+x₂)/2, (y₁+y₂)/2). Example: points (2, 4) and (8, 10) → M = ((2+8)/2, (4+10)/2) = (5, 7). The midpoint is exactly equidistant from both endpoints along the line segment.

Question 2

How do I find the midpoint in 3D?

Accepted Answer

M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). Example: (1,2,3) and (7,8,9) → M = (4, 5, 6). The same averaging principle applies to all three coordinates.

Question 3

How do I find an endpoint given the midpoint and the other endpoint?

Accepted Answer

Rearrange the midpoint formula. If M = (mx, my) and one endpoint is (x₁, y₁): x₂ = 2mx − x₁ and y₂ = 2my − y₁. Example: midpoint (5,7), known endpoint (2,4) → other endpoint = (2×5−2, 2×7−4) = (8, 10).

Question 4

What is the midpoint theorem?

Accepted Answer

The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. It is widely used in coordinate geometry proofs and has applications in construction and engineering.

Question 5

What is the difference between midpoint and distance?

Accepted Answer

The midpoint gives a location — the coordinates of the halfway point. The distance formula gives a measurement — how far apart the two points are. Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2). Distance: d = √((x₂−x₁)² + (y₂−y₁)²).

Point 1	Point 2	Midpoint	Distance
(0, 0)	(4, 6)	(2, 3)	7.211
(-1, 2)	(5, 8)	(2, 5)	8.485
(3, -2)	(9, 4)	(6, 1)	8.485
(0, 0)	(10, 10)	(5, 5)	14.142
(-4, -4)	(4, 4)	(0, 0)	11.314
(2, 7)	(-2, 3)	(0, 5)	5.657
(1, 1)	(7, 9)	(4, 5)	10.000
(0, 5)	(8, -3)	(4, 1)	11.314

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