Answer:
y = -3x +7
Step-by-step explanation:
You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).
Midpoint of BC
The median will go through the midpoint of the segment opposite vertex A. That midpoint is ...
D = (B +C)/2
D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)
Slope
The slope of the line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Then the slope of AD is ...
m = (4 -1)/(1 -2) = 3/-1 = -3
Point-slope equation
The point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation of the line with slope -3 through point A(2, 1) is ...
y -1 = -3(x -2) . . . . . equation of the median line
This can be simplified to slope-intercept form:
y = -3x +6 +1 . . . . . eliminate parentheses, add 1
y = -3x +7 . . . . . slope-intercept equation of the median line
