Three girls are sitting in such a manner that formed a triangle w
| Three girls are sitting in such a manner that formed a triangle with the coordinates of vertices are (3, 1), (2, 3) and (-2, 2). What is the area of formed triangle?
A. 9 Sq. unit
B. 10 Sq. unit
C. 8 Sq. unit
D. 4.5 Sq. unit
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Given:
(x1, y1) = (3, 1), (x2, y2) = (2, 3) and (x3, y3) = (-2, 2)
Concept:
Use of formula for calculating the area of triangle.
Formula used:
\(Area\;of\;\Delta = \frac{1}{2}\;\left[ {\;{x_1}\left( {{y_2}\; - \;{y_3}} \right)\; + \;{x_2}\left( {{y_3}\; - \;{y_1}} \right)\; + \;{x_3}\left( {{y_1}\; - \;{y_2}} \right)} \right]\)
Calculation:
\(Area\;of\;\Delta = \frac{1}{2}\;\left[ {3\;\left( {3\; - \;2} \right)\; + \;2\;\left( {2\; - \;1} \right)\; + \;\left( {\; - 2} \right)\;\left( {1\; - 3} \right)} \right]\;\)
⇒ Area of Δ = 9/2 = 4.5 Sq. unit
∴ The area of formed triangle is 4.5 Sq. unit