Triangle ABC has vertices A(-4,-3),B(4,-1) and C(-2,3). Find the length of median CM?
Find the midpoint of AB,
then use your "distance between two points" formula to get CM .
To find the length of median CM, we first need to determine the coordinates of point M, which is the midpoint of side AB.
The coordinates of point M can be found by averaging the corresponding coordinates of points A and B. Therefore, the x-coordinate of M is (x-coordinate of A + x-coordinate of B)/2, and the y-coordinate of M is (y-coordinate of A + y-coordinate of B)/2.
Let's calculate the coordinates of point M:
x-coordinate of M = (-4 + 4)/2 = 0/2 = 0
y-coordinate of M = (-3 + (-1))/2 = -4/2 = -2/2 = -1
So, the coordinates of point M are (0, -1).
Now that we know the coordinates of point M, we can find the length of median CM. The length of CM is the distance between points C and M, which can be calculated using the distance formula.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points C and M into the formula, we have:
d = √((-2 - 0)^2 + (3 - (-1))^2)
= √((-2)^2 + (3 + 1)^2)
= √(4 + 16)
= √20
= 2√5
Therefore, the length of median CM is 2√5.