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)
To find the equation of the median that passes through point C, we first need to find the coordinates of the midpoint of side AB.
The coordinates of point A are (-2, -2) and the coordinates of point B are (4, 4).
To find the midpoint, we use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-2 + 4)/2, (-2 + 4)/2)
Midpoint = (2/2, 2/2)
Midpoint = (1, 1)
The coordinates of the midpoint of side AB are (1, 1).
Now, we can find the slope of the median passing through C and the midpoint of AB.
The slope of the median passing through C and the midpoint is given by the formula:
m = (y2 - y1)/(x2 - x1)
m = (-4 - 1)/(16 - 1)
m = (-5)/(15)
m = -1/3
So, the slope of the median passing through C and the midpoint is -1/3.
Now, we have the slope and a point (16, -4) on the median. We can use the point-slope form of a linear equation to find the equation of the median:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - (-4) = (-1/3)(x - 16)
y + 4 = (-1/3)(x - 16)
3(y + 4) = -x + 16
3y + 12 = -x + 16
3y = -x + 4
Rearranging the equation to slope-intercept form, we get:
3y = -x + 4
y = (-1/3)x + 4/3
So, the equation of the line containing the median that passes through point C in slope-intercept form is y = (-1/3)x + 4/3.