Question

17) The coordinates of quadrilateral EFGH are E(7, 7), F(4, 8), G(2, 2), H(7, 2). Show that EF is perpendicular to FG.

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Answer 1

see explanation

Explanation:

first we calculate the slopes of EF and FG using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ = E (7, 7 ) and F (4, 8 )

`m_(EF)` =
`(8-7)/(4-7)` =
`(1)/(-3)` = -
`(1)/(3)`

repeat with (x₁, y₁ ) = F (4, 8 ) and (x₂, y₂ ) = G (2, 2 )

`m_(FG)` =
`(2-8)/(2-4)` =
`(-6)/(-2)` = 3

if 2 lines are perpendicular then the product of their slopes = - 1

here

`m_(EF)` ×
`m_(FG)` = -
`(1)/(3)` × 3 = - 1

then EF is perpendicular to FG