Answer:
Look below
Explanation:
To find the length of the median drawn through (5, 1) in the triangle formed by the points (-1, 3), (1, -1), and (5, 1), we need to calculate the distance between (5, 1) and the midpoint of the side opposite to it.
Let's label the given points as follows:
A = (-1, 3)
B = (1, -1)
C = (5, 1)
To find the midpoint of side AB, we use the midpoint formula:
Midpoint AB = ((x_A + x_B) / 2, (y_A + y_B) / 2)
Substituting the coordinates of A and B:
Midpoint AB = ((-1 + 1) / 2, (3 + (-1)) / 2)
= (0 / 2, 2 / 2)
= (0, 1)
So, the midpoint of side AB is M(0, 1).
Now, we can calculate the distance between (5, 1) and M(0, 1) using the distance formula:
Distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2)
Substituting the coordinates of (5, 1) and (0, 1):
Distance = √((5 - 0)^2 + (1 - 1)^2)
= √(5^2 + 0^2)
= √25
= 5
Therefore, the length of the median drawn through (5, 1) is 5 units.