Question

Name the quadrilateral formed by plotting the following points. Also, find the perimeter.

P(5, 2), Q(2, 6), R(2, −6), S(5, −2)

Answer 1

Given:

P(5, 2), Q(2, 6), R(2, −6), S(5, −2)

Step 1: Find Side Lengths Using Distance Formula

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

PQ = `sqrt((2 − 5)^2 + (6 − 2)^2)`

= `sqrt(9 + 16)`

`sqrt25`

= 5

QR: `sqrt((2 − 2)^2 + (−6 − 6)^2)`

= `sqrt(0 + 144)`

== `sqrt144`

= 12

RS = `sqrt((5 − 2)^2 + (−2 + 6)^2)`

= `sqrt(9 + 16)`

= `sqrt25`

= 5

SP = `sqrt((5 − 5)^2 + (2 + 2)^2)`

= `sqrt0 + 16`

= `sqrt16`

= 4

Step 2: Identify the Quadrilateral

One pair of opposite sides is equal and parallel (PQ = RS = 5)

The other pair is unequal (QR = 12, SP = 4)

Figure = Isosceles Trapezium

Perimeter = PQ + QR + RS + SP

= 5 + 12 + 5 + 4

= 26 units