Question

On a coordinate plane, rectangle E F G H is shown. Point E is at (1, negative 1), point F is at (negative 4, 1), point G is at (negative 3, 4), and point H is at (2, 2). What is the perimeter of rectangle EFGH? StartRoot 10 EndRoot + StartRoot 29 EndRoot units 2 StartRoot 10 EndRoot + 2 StartRoot 29 EndRoot units 22 units 39 units

Answer 1

D

Explanation:

Answer 2

Perimeter of rectangle=
`2 (√(10) + √(29))`

=
`2√(10) + 2√(29)`.

Explanation:

Given:
`E(x_(1), y_(1)) = (1. -1), F(x_(2), y_(2)) = (-4, 1), G(x_(3), y_(3)) = (-3, 4), H(x_(4), y_(4)) = (2, 2)`

Using distance formula:

Length of EF =
`\sqrt{(x_(2) - x_(1) )^2 + (y_(2) - y_(1))^2}`

=
`√((-4 - 1)^2 + (1 - (-1))^2)`

=
`√((-4 - 1)^2 + (1 + 1))^2)`

=
`√((-5)^2 + (2))^2)`

=
`√(25 + 4)`

=
`√(29)`

Length of FG =
`\sqrt{(x_(3) - x_(2) )^2 + (y_(3) - y_(2))^2}`

=
`√((-3 - (-4)^2 + (4 - 1)^2)`

=
`√((1)^2 + (3)^2)`

=
`√(1 + 9)`

=
`√(10)`

Length of GH =
`\sqrt{(x_(4) - x_(3) )^2 + (y_(4) - y_(3))^2}`

=
`√((2 - (-3))^2 + (2 - 4)^2)`

=
`√((5)^2 + (-2))^2)`

=
`√(25 + 4)`

=
`√(29)`

Length of HE =
`\sqrt{(x_(4) - x_(1) )^2 + (y_(4) - y_(1))^2}`

=
`√((2 - 1)^2 + (2 - (-1))^2)`

=
`√((1)^2 + (3)^2)`

=
`√(1 + 9)`

=
`√(10)`

∵ EFGH is a rectangle ∴ EH = FG and EF = HG

Perimeter of rectangle = 2 ( EF + FG + GH + HE)

= 2 (EF + FG)

=
`2 (√(10) + √(29))`

=
`2√(10) + 2√(29)`

Therefore option (b) is the correct answer.