Question

Name the figure formed by plotting the following points. Also, find the area of the figure.

P(2, 7), Q(−3, 1), R(2, 4), S(7, 1)

Answer 1

Given:

P(2, 7), Q(−3, 1), R(2, 4), S(7, 1)

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

PQ = `sqrt((2 − (−3))^2 + (7 − 1)^2)`​ 

= `sqrt(25 + 36)`​ 

= `sqrt61​`

QR = `sqrt((2 − (−3))^2 + (4 − 1)^2)`

​= `sqrt(25 + 9)​`

= `sqrt34`

RS = `sqrt((7 − 2)^2 + (1 − 4)^2)`

= `sqrt(25+9)`

​= `sqrt34`

SP = `sqrt((7 − 2)^2 + (1 − 7)^2)`

= `sqrt(25 + 36)`

= `sqrt61`

Diagonals:

PR: `sqrt((2 − 2)^2 + (7 − 4)^2)`

= `sqrt(0 + 9)`

= 3

QS = `sqrt((7 − (−3))^2 + (1 − 1)^2)`

= `sqrt(100 + 0)`

= 10

Step 3:

Opposite sides are equal:

PQ  = SP = `sqrt61,` and QR = RS = `sqrt34`

Diagonals are not equal:

PR = 3, QS = 10 

Therefore, the figure is an arrowhead.

Step 4: Find Area of Arrowhead

Area of a kite = `1/2​ xx d_1 xx d_2`

d1 = PR = 3

d2 = QS = 10

 Area = `1/2 xx 3 xx 10`

Area = 15 square units