triangle CAT has vertices C(4,9), A(8,-9),T(-6,5) M is the midpoint of TA . find the length of the median CM
To find the length of the median CM, we need to first find the coordinates of point M, which is the midpoint of side TA. Then, we can calculate the distance between points C and M to get the length of the median CM.
Step 1: Find the coordinates of point M (the midpoint of TA).
The midpoint of a line segment can be found by averaging the x-coordinates and y-coordinates of the two endpoints. Let's find the x-coordinate of point M:
x-coordinate of M = (x-coordinate of T + x-coordinate of A) / 2
= (-6 + 8) / 2
= 2 / 2
= 1
Now, let's find the y-coordinate of point M:
y-coordinate of M = (y-coordinate of T + y-coordinate of A) / 2
= (5 - 9) / 2
= -4 / 2
= -2
Thus, the coordinates of point M are (1, -2).
Step 2: Calculate the distance between points C and M.
To find the length of the median CM, we need to calculate the distance between points C(4, 9) and M(1, -2). We can use the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Plugging in the coordinates, we have:
Distance = √[(1 - 4)² + (-2 - 9)²]
= √[(-3)² + (-11)²]
= √[9 + 121]
= √130
Thus, the length of the median CM is √130 units.