Question

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are:
(i) y = x, y = 2x and y + x = 6
(ii) y = x, 3y = x, x + y = 8

Answer 1

Triangle

Step-by-step explanation:

(i) y = x, y = 2x and y + x = 6

To draw y = x, we will plot the points (1,1) and (0,0).

To draw y = 2x, we will plot the points (1,2) and (0,0).

To draw x + y = 6, we will plot the points (0,6) and (6,0).

The shaded region is the triangle formed by the 3 lines.

 = Area of ∆ABC - Area of  ∆ADC

 = 1/2 height of ∆ABC * AC +  1/2 height of ∆ADC * AC  

 = 1/2 * 4 * 6 + 1/2 * 3 * 6

 = 21 sq. cm.

Vertices of ∆ABD are A(0,0) , B(2,4), D(3,3). Please refer the attached picture for the graph.

(ii) y = x, 3y = x, x + y = 8 --- Please solve using similar steps.