Given triangle ABC with A(-4,-2), B(4,4), and C(18,-8), answer the question. Write the equation of the line containing the median that passes through B in standard form.
To find the equation of the line containing the median passing through point B, we need to first find the midpoint of side AC, which is the centroid of triangle ABC.
The coordinates of the midpoint M of side AC can be found by taking the average of the x-coordinates and the average of the y-coordinates.
x-coordinate of M: (x_A + x_C) / 2 = (-4 + 18) / 2 = 14 / 2 = 7
y-coordinate of M: (y_A + y_C) / 2 = (-2 + (-8)) / 2 = -10 / 2 = -5
So, the midpoint M of side AC is M(7, -5).
Now, we can find the equation of the line containing the median passing through point B. We have two points on the line: B(4, 4) and M(7, -5). We can use the point-slope form of a linear equation to find the equation of the line.
The slope of the line passing through B and M can be found using the formula:
slope = (y_2 - y_1) / (x_2 - x_1) = (-5 - 4) / (7 - 4) = -9 / 3 = -3
Using the point-slope form, the equation of the line is:
y - y_1 = m(x - x_1)
y - 4 = -3(x - 4)
Expanding and simplifying this equation:
y - 4 = -3x + 12
y = -3x + 16
Converting this equation to standard form:
3x + y = 16