Question

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Answer 1

Answer:

y = - x + 6

Step-by-step explanation:

-- Rhombus diagonals are perpendicular and bisect each other.

-- A( $x_{1}$ , $y_{1}$ ) and B( $x_{2}$ , $y_{2}$ )

Coordinates of the midpoint of a segment AB are

( $\frac{x_{1} +x_{2} }{2}$ , $\frac{y_{1} +y_{2} }{2}$ )

and formula of a slope of the line segment AB is

m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

-- If AB ⊥ CD then $m_{AB}$ × $m_{CD}$ = - 1

-- Slope-point of linear equation is

y - $y_{1}$ = m( x - $x_{1}$ )

~~~~~~~~~~~~~~~~

M(0, 2)

T(4, 6)

$m_{MT}$ = $\frac{6-2}{4-0}$ = 1

$m_{AH}$ = - 1

Coordinates of the intersection of the diagonals are ( $\frac{4+0}{2}$ , $\frac{6+2}{2}$ ) = (2, 4)

y - 4 = - 1(x - 2)

y = - x + 6 is slope-intercept form of the diagonal AH