Solution Found!
(a) Prove that the midpoint of the line segment from P1sx1, y1, z1d to P2sx2, y2, z2 d
Chapter 8, Problem 17(choose chapter or problem)
QUESTION:
(a) Prove that the midpoint of the line segment from P1sx1, y1, z1d to P2sx2, y2, z2 d is S x1 1 x2 2 , y1 1 y2 2 , z1 1 z2 2 D (b) A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices As1, 2, 3d, Bs22, 0, 5d, and Cs4, 1, 5d.
Questions & Answers
QUESTION:
(a) Prove that the midpoint of the line segment from P1sx1, y1, z1d to P2sx2, y2, z2 d is S x1 1 x2 2 , y1 1 y2 2 , z1 1 z2 2 D (b) A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices As1, 2, 3d, Bs22, 0, 5d, and Cs4, 1, 5d.
ANSWER:(a) We need to prove that the coordinates of the midpoint are S x1 1 x2 2 , y1 1 y2 2 , z1 1 z2 2 D.
We start by showing that the x-coordinate of the midpoint is x1 1 x2 2:
We know that the formula for the midpoint of a line segment is given by MP x1 1 x2 2 , y1 1 y2 2 D.
So, the x-coordinate of the midpoint, MPx can be written as follows:
MPx x1 1 x2 2
Since the x-coordinates of the two points, P1 and P2, are given as x1 and x2 respectively, we can substitute them in