Triangle ABC has the following points: A (-2,-2), B (4,4), C (16,-4). Use these points to write the equation of the line containing the median that passes through point C in SLOPE INTERCEPT FORM. Make sure to show all work in order to receive full points. (3 points)
First, let's find the coordinates of the midpoint of side AB, which is the median.
The x-coordinate of the midpoint (Mx) is the average of the x-coordinates of A and B:
Mx = (Ax + Bx)/2 = (-2 + 4)/2 = 2/2 = 1
Similarly, the y-coordinate of the midpoint (My) is the average of the y-coordinates of A and B:
My = (Ay + By)/2 = (-2 + 4)/2 = 2/2 = 1
So, the coordinates of the midpoint M are (1,1).
Now, we have two points on the line containing the median; C (16, -4) and M (1,1).
We can use the slope formula to find the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (-4 - 1) / (16 - 1)
m = -5 / 15
m = -1/3
Using the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values we know to find the equation of the line:
Using point C, we know that x = 16 and y = -4:
-4 = (-1/3)(16) + b
-4 = -16/3 + b
b = -4 + 16/3
b = -12/3 + 16/3
b = 4/3
So, the equation of the line containing the median that passes through point C is:
y = (-1/3)x + 4/3