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QuestionLocate points of rectangle ABCDABCD at A(2,2),B(2,−1),C(−1,−1),D(−1,2)A(2,2), B(2,-1), C(-1,-1), D(-1,2), then find its perimeter and area.

Studdy Solution

STEP 1

Assumptions1. The vertices of the rectangle are located at A(,),B(,−1)A(,), B(,-1), C(−1,−1)C(-1,-1), and (−1,)(-1,). . The rectangle sides are parallel to the axes.
3. The distance between two points (x1,y1)(x1, y1) and (x,y)(x, y) is given by the formula \sqrt{(x-x1)^ + (y-y1)^}.
4. The perimeter of a rectangle is given by the formula (length+width)(length + width).
5. The area of a rectangle is given by the formula length×widthlength \times width.

STEP 2

First, we need to find the lengths of the sides of the rectangle. We can do this by using the distance formula between two points. Let's start with the length of side ABAB.
AB=(x2−x1)2+(y2−y1)2AB = \sqrt{(x2-x1)^2 + (y2-y1)^2}

STEP 3

Now, plug in the given values for the coordinates of points AA and BB to calculate the length of side ABAB.
AB=(2−2)2+(−1−2)2AB = \sqrt{(2-2)^2 + (-1-2)^2}

STEP 4

Calculate the length of side ABAB.
AB=(0)2+(−3)2=9=3AB = \sqrt{(0)^2 + (-3)^2} = \sqrt{9} =3

STEP 5

Next, calculate the length of side BCBC using the same distance formula.
BC=(x2−x1)2+(y2−y1)2BC = \sqrt{(x2-x1)^2 + (y2-y1)^2}

STEP 6

Plug in the given values for the coordinates of points BB and CC to calculate the length of side BCBC.
BC=(−1−2)2+(−1−(−1))2BC = \sqrt{(-1-2)^2 + (-1-(-1))^2}

STEP 7

Calculate the length of side BCBC.
BC=(−3)2+(0)2=9=3BC = \sqrt{(-3)^2 + (0)^2} = \sqrt{9} =3

STEP 8

Now that we have the lengths of the sides, we can find the perimeter of the rectangle. The perimeter of a rectangle is given by the formula 2(length+width)2(length + width).
Perimeter=2(AB+BC)Perimeter =2(AB + BC)

STEP 9

Plug in the values for the lengths of sides ABAB and BCBC to calculate the perimeter.
Perimeter=2(3+3)Perimeter =2(3 +3)

STEP 10

Calculate the perimeter of the rectangle.
Perimeter=2(6)=12Perimeter =2(6) =12

STEP 11

Now that we have the lengths of the sides, we can also find the area of the rectangle. The area of a rectangle is given by the formula length×widthlength \times width.
Area=AB×BCArea = AB \times BC

STEP 12

Plug in the values for the lengths of sides ABAB and BCBC to calculate the area.
Area=×Area = \times

STEP 13

Calculate the area of the rectangle.
Area=9Area =9The perimeter of the rectangle is12 units and the area is9 square units.

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