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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

User Tstojecki
by
8.5k points

2 Answers

6 votes

Answer:

D

Explanation:

User David Brewer
by
8.5k points
4 votes

Answer:

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.

User Andrew Noonan
by
8.8k points

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