Question

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the median of the triangle with vertices A(1,2,3), B(-2,0,5), and C(4,1,5)

Answer 1

To find the length of the median of a triangle, we need to find the midpoint of the side opposite to the vertex. Given the vertices A(1,2,3), B(-2,0,5), and C(4,1,5), the length of the median AM is 2.5 units.

Step-by-step explanation:

To find the length of the median of a triangle, we need to find the midpoint of the side opposite to the vertex. Given the vertices of the triangle A(1,2,3), B(-2,0,5), and C(4,1,5), we can find the length of the median by finding the midpoint of the side BC.

The coordinates of the midpoint M can be found by averaging the coordinates of points B and C: M = ((-2 + 4)/2, (0 + 1)/2, (5 + 5)/2) = (1, 0.5, 5). Now, we can find the length of the median AM using the distance formula: AM = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2) = √((1 - 1)^2 + (2 - 0.5)^2 + (3 - 5)^2) = √(0 + 1.5^2 + (-2)^2) = √(2.25 + 4) = √6.25 = 2.5 units.