Question

What is the perimeter in square units of the rectangle shown on the coordinate grid?

Answer 1

A

Explanation:

The opposite sides of a rectangle are congruent.

Calculate the lengths of 2 of the sides using the distance formula and multiply by 2

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 10) and (x₂, y₂ ) = (2, 7)

d =
`√((2+2)^2+(7-10)^2)`

=
`√(4^2+(-3)^2)`

=
`√(16+9)` =
`√(25)` = 5

Repeat

with (x₁, y₁ ) = (- 8, 2) and (x₂, y₂ ) = (- 2, 10)

d =
`√((-2+8)^2+(10-2)^2)`

=
`√(6^2+8^2)`

=
`√(36+64)` =
`√(100)` = 10

Hence

Perimeter = (2 × 5) + (2 × 10) = 10 + 20 = 30 units → A

Answer 2

In order to find the Perimeter of the Rectangle, First we need to find the Length and Width of the Rectangle.

Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

`\bigstar\;\; \mathsf{Distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2)}`

There are two lengths in a rectangle. Let us find any one length of the rectangle.

I'm considering the length with co-ordinates (-8 , 2) and (-2 , 10)

Here : x₁ = -8 and x₂ = -2 and y₁ = 2 and y₂ = 10

Substituting the values in the distance formula, We get :

`\mathsf{\implies Length = √([-2 - (-8)]^2 + [10 - 2]^2)}`

`\mathsf{\implies Length = √([-2 + 8]^2 + [8]^2)}`

`\mathsf{\implies Length = √([6]^2 + [8]^2)}`

`\mathsf{\implies Length = √(36 + 64)}`

`\mathsf{\implies Length = √(100)}`

`\mathsf{\implies Length = 10}`

There are two widths in a rectangle. Let us find any one width of the rectangle.

I'm considering the width with co-ordinates (-2 , 10) and (2 , 7)

Here : x₁ = -2 and x₂ = 2 and y₁ = 10 and y₂ = 7

Substituting the values in the distance formula, We get :

`\mathsf{\implies Width = √([2 - (-2)]^2 + [7 - 10]^2)}`

`\mathsf{\implies Width = √([2 + 2]^2 + [-3]^2)}`

`\mathsf{\implies Width = √([4]^2 + [-3]^2)}`

`\mathsf{\implies Width = √(16 + 9)}`

`\mathsf{\implies Width = √(25)}`

`\mathsf{\implies Width = 5}`

Perimeter of a Rectangle is given by : 2[Length + Width]

`:\implies` Perimeter of the given rectangle = 2[10 + 5]

`:\implies` Perimeter of the given rectangle = 2[15]

`:\implies` Perimeter of the given rectangle = 30

Answer : Perimeter of the given rectangle is 30 square units