Final answer:
To find the equation of the median from B in the given triangle, calculate the midpoint of AC, then use its coordinates along with B's to determine the slope of the median. Finally, apply the slope and one point to form the equation, which is y = -7x + 23.
Step-by-step explanation:
To determine the equation of the median from B in a triangle with vertices A(-3, 7), B(4, -5), and C(9, -3), we first find the midpoint of AC. The midpoint, M, has coordinates ((-3+9)/2, (7-3)/2) = (3, 2). The median from point B will pass through this point, and B itself.
The slope of the median can be calculated using the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we get m = (2 - (-5)) / (3 - 4) = 7 / -1 = -7.
Now that we have the slope, we can use the point-slope form of a line to get the equation of the median. The point-slope form is y - y1 = m(x - x1). Using point B(4, -5) and slope -7, the equation is:
y - (-5) = -7(x - 4)
Finally, we simplify this to get the standard form of the equation: y = -7x + 28 - 5 = -7x + 23. Therefore, the equation of the median from B is y = -7x + 23.