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 find the coordinates of point M first.
Step 1: Find the midpoint M of TA.
To find the midpoint of two points (x1, y1) and (x2, y2), use the following formulas:
Midpoint x-coordinate: (x1 + x2) / 2
Midpoint y-coordinate: (y1 + y2) / 2
In this case, the coordinates of point T are (-6, 5) and the coordinates of point A are (8, -9).
Midpoint x-coordinate: (-6 + 8) / 2 = 2 / 2 = 1
Midpoint y-coordinate: (5 + (-9)) / 2 = -4 / 2 = -2
So, the coordinates of point M are (1, -2).
Step 2: Find the length of the median CM.
To find the length of the median, we need to calculate the distance between points C(4, 9) and M(1, -2).
Distance formula:
√((x2 - x1)^2 + (y2 - y1)^2)
Distance CM: √((1 - 4)^2 + (-2 - 9)^2)
= √((-3)^2 + (-11)^2)
= √(9 + 121)
= √(130)
≈ 11.40
Therefore, the length of the median CM is approximately 11.40 units.