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.

Answer 1

Answer:

see explanation

Step-by-step explanation:

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

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

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

$m_{EF}$ = $\frac{8-7}{4-7}$ = $\frac{1}{-3}$ = - $\frac{1}{3}$

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

$m_{FG}$ = $\frac{2-8}{2-4}$ = $\frac{-6}{-2}$ = 3

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

here

$m_{EF}$ × $m_{FG}$ = - $\frac{1}{3}$ × 3 = - 1

then EF is perpendicular to FG