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.
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 x-coordinate of the midpoint is the average of the x-coordinates of points A and B:
Midpoint x-coordinate = (x-coordinate of A + x-coordinate of B) / 2 = (-2 + 4) / 2 = 2 / 2 = 1
The y-coordinate of the midpoint is the average of the y-coordinates of points A and B:
Midpoint y-coordinate = (y-coordinate of A + y-coordinate of B) / 2 = (-2 + 4) / 2 = 2 / 2 = 1
Therefore, the midpoint of side AB is M(1, 1).
Now that we have the coordinates of point C (16, -4) and the midpoint M(1, 1), we can find the slope of the line containing the median by using the slope formula:
slope = (y2 - y1) / (x2 - x1), where (x1, y1) is the midpoint M(1, 1) and (x2, y2) is point C (16, -4).
slope = (-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:
Using the point (16, -4), we have -4 = (-1/3)(16) + b.
Simplifying, -4 = -16/3 + b.
To find b, we bring -16/3 to the other side by adding 16/3 to both sides:
-4 + 16/3 = b.
-12/3 + 16/3 = b.
4/3 = b.
So, b = 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.