Question

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically : 
(i) the area of a triangle;
(ii) the coordinates of the vertices of the triangle.

Answer 1

y - 2 = 0
⇒ y = 2
y + 1 = 3(x - 2)
⇒ y + 1 = 3x - 6
⇒ y = 3x - 6 - 1
⇒ y = 3x - 7
The table for y + 1 = 3(x - 2) is 

X	1	2	3
Y	- 4	- 1	2

Also we have
x + 2y = 0
⇒ x = - 2y
The table for x + y = 0 is

X	- 4	4	- 6
Y	2	- 2	3

Plotting the above points we get the folllowing required graph:

(i) The area of the triangle ABC = `(1)/(2) xx "AB" xx "CD"`

= `(1)/(2) xx 7 xx 3`

=  `(21)/(2)`

= 10.5 sq.units

(ii) The coordinates of the verticles of the triangle are ( - 4, 2), (3, 2) and (2, -1).