Question

a(4 7) b(9 7) c(6 3) d(1 3) plot the points in a graph sheet and identify the quadrilateral.Verify using distance formula and find its area​

Answer 1

Step-by-step explanation:

Given a(4 7) b(9 7) c(6 3) d(1 3) plot the points in a graph sheet and identify the quadrilateral.Verify using distance formula and find its area​

• let the points be a(4,7), b(9,7), c(6,3) and d(1,3)
• now we need to find the distance ab, bc, cd and ad
• by applying distance formula we get
• so ab = √(x2 – x1)^2 + (y2 – y1)^2
•          = √(9 – 4)^2 + (7 – 7)^2
•         = √5^2 + 0
•          = √25
•         = 5
• So bc = so ab = √(x2 – x1)^2 + (y2 – y1)^2
•          = √(6 – 9)^2 + (3 – 7)^2
•         = √-3^2 + (-4)^2
•          = √25
•         = 5
• so cd = √(x2 – x1)^2 + (y2 – y1)^2
•          = √(1 – 6)^2 + (3 – 3)^2
•         = √5^2 + 0
•          = √25
•         = 5
• so ad = √(x2 – x1)^2 + (y2 – y1)^2
•          = √(1 – 4)^2 + (3 – 7)^2
•         = √(-3)^2 + (-4)^2
•          = √25
•         = 5
• Since ab = bc = cd = ad = 5
• So all sides of quadrilateral are equal and so it can be a square or a rhombus.
• Therefore we need to find the length of diagonals of the quadrilateral ac and bd.
• Now ac = (4,7) (6,3)
• Applying distance formula we get
• So ac = √(6 – 4)^2 + (3 – 7)^2
•          = √2^2 + (-4)^2
•         = √4 + 16
•               = √20
•             = 2√5
• Now bd = (9,7) (1,3)
• Applying distance formula we get
• So bd = √(1 – 9)^2 + (3 – 7)^2
•          = √(-8)^2 + (-4)^2
•         = √64 + 16
•               = √80
•             = 4√5
• Since the diagonal is twice the other it is a rhombus.
• Now area of the rhombus = ½ (diagonals)
•                                              = ½ (2√5 x 4√5)
•                                            =     4 x 5
•                                            =20 sq units

Reference link will be

https://brainly.in/question/7737285

Answer 2

given: co-ordinates a(4 7) b(9 7) c(6 3) d(1 3) are given to draw graph.

find: identify the quadrilateral and verify using distance formula and find its area​.

solution:

step 1:

draw the graph with the given co-ordinates. graph is shown in attached file.

given co-ordinates are: a(4 7) b(9 7) c(6 3) d(1 3)

step 2:

we have to find the distance ab,bc,cd,ad by using distance formula.

to find ab:

x₁ = 4, y₁ = 7, x₂ = 9 , y₂= 7.

ab = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(9-4)² + (7-7)²

    = √(5)² + 0

 ab  = 5

step 3:

to find bc:

x₁ = 9, y₁ = 7, x₂ = 6 , y₂= 3.

bc = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(6-9)² + (3-7)²

    = √(-3)² + (-4)²

   =√9 + 16

   = √25

 bc  = 5

step 4:

to find cd:

x₁ = 6, y₁ = 3, x₂ = 1 , y₂= 3.

cd = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(1-6)² + (3-3)²

    = √(-5)² + (0)²

   =√25

 cd  = 5

step 5:

to find da:

x₁ = 1, y₁ = 3, x₂ = 4 , y₂= 7.

da = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(4-1)² + (7-3)²

    = √(3)² + (4)²

    = √9 + 16

   =√25

 da  = 5

since ab=bc=cd=da=5.

all sides of quadrilateral are equal. so it can be a rhombus or square.

step 6:

now we will find the length of diagonals ie. ac and bd.

to find ac:

x₁ = 4, y₁ = 7, x₂ = 6 , y₂= 3.

ac = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(6-4)² + (3-7)²

    = √(2)² + (-4)²

    = √4 + 16

ac =√20

 ac  = 4.47

step 7:

to find bd:

x₁ = 9, y₁ = 7, x₂ = 1 , y₂= 3.

bd = √(x₂ - x₁)² + (y₂ - y₁)²

    = √(1-9)² + (3-7)²

    = √(-8)² + (-4)²

    = √64 + 16

   =√80

   =√20*4

   = 2√20

bd = 8.94

diagonals are not equal. so it is a rhombus.

step 8:

area of rhombus is: $\frac{1}{2}$ * d₁ ˣ d₂.

d₁ = ac = 4.47

d₂ = bd = 8.94

so area is:  $\frac{1}{2}$ * 4.47 ˣ 8.94 = 19.9 sq. units

ANS:

this quadrilateral is a rhombus. and area is 19.9 sq. units.