Question

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)

Answer 1

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