The vertices of a triangle are L(1,3), M(4,0), N(-4,1)
LO is a median of the triangle. What are the coordinates of point O? Explain.
O = (0,1/2)
O is midway between M and N, so its coordinates are the average of M and N.
To find the coordinates of point O, we need to calculate the midpoint of segment LM, which serves as the median of the triangle.
The midpoint formula is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's calculate the coordinates of point O step by step:
1. Identify the coordinates of points L and M:
L(1, 3)
M(4, 0)
2. Apply the midpoint formula to find the coordinates of point O:
x-coordinate of O = (1 + 4) / 2 = 5 / 2 = 2.5
y-coordinate of O = (3 + 0) / 2 = 3 / 2 = 1.5
Therefore, the coordinates of point O, which is the midpoint of segment LM and also the median of the triangle, are O(2.5, 1.5).