draw the graphs of equation 2 x - Y =1 and 3 X + 2 Y =12 determine the vertices of the Triangle formed by the triangle representing the equation and the x axis shade the triangular region so formed also find its area
Answers
EXPLANATION.
Draw Graph of the equation.
⇒ 2x - y = 1. - - - - - (1).
⇒ 3x + 2y = 12. - - - - - (2).
As we know that,
Form equation (1), we get.
⇒ 2x - y = 1. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) - y = 1.
⇒ - y = 1.
⇒ y = - 1.
Their Co-ordinates = (0,-1).
Put the value of y = 0 in the equation, we get.
⇒ 2x - (0) = 1.
⇒ 2x = 1.
⇒ x = 1/2.
⇒ x = 0.5.
Their Co-ordinates = (0.5,0).
From equation (2), we get.
⇒ 3x + 2y = 12. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 3(0) + 2y = 12.
⇒ 2y = 12.
⇒ y = 6.
Their Co-ordinates = (0,6).
Put the value of y = 0 in the equation, we get.
⇒ 3x + 2(0) = 12.
⇒ 3x = 12.
⇒ x = 4.
Their Co-ordinates = (4,0).
Both curves intersects at a point = (2,3).
As we know that,
⇒ Area of triangle = 1/2 x Base x Height.
⇒ Height = 3 cm.
⇒ Base = 4 - 0.5 = 3.5 cm.
Put the values in the equation, we get.
Area of triangle = 1/2 x 3.5 x 3.
Area of triangle = 5.25 sq. units.
