Question

a quadrillateral has sides with equations y = -2x, 2x+y=6, y=1/2x+6, and x-2y=9. is the figure a rectangle? explain your reasoning

Answer 1

A) y = -2x ⇒ slope (m) =
`(-2)/(1)`

B) 2x + y = 6

-2x -2x

y = -2x + 6 ⇒ slope (m) =
`(-2)/(1)`

C) y =
`(1)/(2)`x + 6 ⇒ slope (m) =
`(1)/(2)`

D) x - 2y = 9

-x -x

-2y = -x + 9

`(-2)/(-2)`y =
`(-1)/(-2)`x +
`(9)/(-2)`

y =
`(1)/(2)`x - 4.5 ⇒ slope (m) =
`(1)/(2)`

A rectangle has 90° angles so two slopes must be the same and the other two slopes must be perpendicular (opposite sign and reciprocal) to the first two slopes.

Slopes:
`(-2)/(1)`,
`(-2)/(1)`,
`(1)/(2)`,
`(1)/(2)`.

Answer: YES. Two lines have a slope of
`(1)/(2)`and the other two lines have a perpendicular slope of
`(-2)/(1)`,