x+y=6 What is the area of the triangle formed from the x axis and the y axis?
Answers
54
How do I calculate the area of a triangle formed by the x-axis, the y-axis and the line 3x-y-6=0?
David Kenneth Richardson
Answered January 10, 2017
The x and y axes automatically become the height and base of the triangle. The diagonal line 3x - y - 6 = 0 will determine what lengths they have.
To do this, we need to put it in y = mx + b format:
3x−y−6=0
3x−y=6
−y=6−3x
y=3x−6
It crosses the y -axis at:
y=3x−6
y=3(0)−6
y=0−6
x = 2
(0, -6)
It crosses the x-axis at:
y=3x−6
0=3x−6
6=3x
x = 2
(2, 0)
So we have a triangle with a base of 2 units and a height of | - 6| = 6 units. We can now find the area:
A=12bh
A=12(2)(6)
A=6 square units
Step-by-step explanation:
It is just simple one. The given line x +y +6 =0 cuts the x- y, co-ordinate axes at the points
A(-6, 0) , B(0, -6) respectively and it makes a right- angled triangle OAB with the co-ordinate axes .where O is origin (0,0). Therefore required area of the triangle OAB
= (1/2) OA· OB = (1/2)(6)(6) = 18 sq.unit .