Given ABC with A(-4, -2), B(4, 4), and C (18, -8), answer the question write the equation for the line containing the median that passes through point C in slope intercept form
To find the equation for the line containing the median passing through point C, we first need to find the coordinates of the midpoint of side AB. The midpoint formula is:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
For points A(-4, -2) and B(4, 4), the coordinates of the midpoint are:
Midpoint = [(-4 + 4)/2, (-2 + 4)/2]
= [0/2, 2/2]
= [0, 1]
The midpoint of side AB is (0, 1).
Now, let's find the slope of the line passing through point C(18, -8) and the midpoint (0, 1):
Slope (m) = (y2 - y1)/(x2 - x1)
= (-8 - 1)/(18 - 0)
= (-9)/18
= -1/2
We can use the point-slope form of a linear equation to find the equation of the line containing the median passing through point C:
y - y1 = m(x - x1)
Using the coordinates of point C (18, -8), the equation becomes:
y - (-8) = (-1/2)(x - 18)
Simplifying:
y + 8 = (-1/2)(x - 18)
Now, let's convert the equation to slope-intercept form (y = mx + b):
y + 8 = (-1/2)x + 9
y = (-1/2)x + 9 - 8
y = (-1/2)x + 1
Therefore, the equation for the line containing the median passing through point C in slope-intercept form is y = (-1/2)x + 1.