Question

Triangle ABC has the following points: A (-2,-2), B (4,4), C (16,-4). Use these points to write the equations of the line containing the median that passes through point C in slope-intercept form.

Answer 1

To find the equation of the median that passes through point C, we need to find the midpoint of the side opposite to point C (side AB).

The coordinates of the midpoint of AB can be found by averaging the coordinates of A and B:

Midpoint AB = ((-2+4)/2, (-2+4)/2) = (1, 1)

Now that we have the midpoint, we can find the slope of the median using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (1, 1) and (x2, y2) = (16, -4):

slope = (-4 - 1) / (16 - 1) = -5/15 = -1/3

Since the median passes through point C with coordinates (16, -4), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1), where (x1, y1) = (16, -4) and m = -1/3

y + 4 = (-1/3)(x - 16)

y + 4 = (-1/3)x + 16/3

y = (-1/3)x + 16/3 - 12/3

y = (-1/3)x + 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.