Triangle ABC has the following points: A (-2,-2), В (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.
To find the equation of the line containing the median that passes through point C, we first need to find the coordinates of the midpoint of side AB.
The midpoint formula is given by:
(xMid, yMid) = ((x1 + x2) / 2, (y1 + y2) / 2)
Using the points A(-2, -2) and B(4, 4), we can find the midpoint as follows:
xMid = (-2 + 4) / 2 = 2 / 2 = 1
yMid = (-2 + 4) / 2 = 2 / 2 = 1
So, the midpoint of side AB is (1, 1).
Next, we need to find the slope of the line passing through points C(16, -4) and the midpoint (1, 1).
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the points C(16, -4) and (1, 1):
m = (-4 - 1) / (16 - 1) = -5 / 15 = -1/3
Now we can write the equation of the line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Using the slope-intercept form, we substitute the slope (-1/3) and the coordinates of point C (16, -4) to solve for the y-intercept b:
-4 = (-1/3)(16) + b
-4 = -16/3 + b
To solve for b, we can add 16/3 to both sides:
b = -4 + 16/3 = -12/3 + 16/3 = 4/3
Therefore, the equation of the line containing the median that passes through point C in slope-intercept form is:
y = (-1/3)x + 4/3