Question

/_\ DEF has vertices D(-2,4), E(0,-2), and F(6,2). Determine:
a) an equation for DG, the median from D to EF
b) an equation for FC, the altitude from F to DE
c) an equation for AB, the right bisector of DF

Answer 1

(a)
G is midpoint of EF = ((0+6)/2, (-2+2)/2) = (3,0)

Equation of line DG is y-4 = m(x+2), where m = slope of DG

m = ( y1-y2)/(x1-x2) = (4-0)/(-2-3) = -4/5

DG is the line y - 4 = -(4/5)(x + 2), so 5y - 20 = -4x - 8

DG is 4x + 5y - 12 = 0

Answer 2

(b)
FC perpendicular to DE. Slope of DE = (4--2)/(-2-0) 6/(-2) = -3

so slope of FC = 1/3 (remember m_1 times m_2 = -1)

So equation of line FC is y-2 = (1/3)(x-6)

3y - 6 = x - 6

FC is 3y - x = 0

Answer 3

(c)
Mid point of DF = ((-2+6)/2, (4+2)/2) = (2,3)

Slope of DF = (4-2)/(-2-6) = -2/8 = -1/4, so slope of right bisector = 4

AB is the line y-3 = 4(x - 2), or

y + 4x +5 = 0