Answer:
y = - x + 6
Step-by-step explanation:
-- Rhombus diagonals are perpendicular and bisect each other.
-- A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of the midpoint of a segment AB are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
and formula of a slope of the line segment AB is
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
-- If AB ⊥ CD then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1
-- Slope-point of linear equation is
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~
M(0, 2)
T(4, 6)
[tex]m_{MT}[/tex] = [tex]\frac{6-2}{4-0}[/tex] = 1
[tex]m_{AH}[/tex] = - 1
Coordinates of the intersection of the diagonals are ( [tex]\frac{4+0}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = (2, 4)
y - 4 = - 1(x - 2)
y = - x + 6 is slope-intercept form of the diagonal AH
