Question

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In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0, 2) and T(4, 6). Write an equation of the line that contains diagonal AH. Give your answer in slope-intercept form.

Answer 1

y = - x + 6

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

(
`(x_(1) +x_(2) )/(2)` ,
`(y_(1) +y_(2) )/(2)` )

and formula of a slope of the line segment AB is

m =
`(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)` =
`(6-2)/(4-0)` = 1

`m_(AH)` = - 1

Coordinates of the intersection of the diagonals are (
`(4+0)/(2)` ,
`(6+2)/(2)` ) = (2, 4)

y - 4 = - 1(x - 2)

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