Question

Question 2
Determine graphically, the vertices of the triangle formed by the lines
y = x, 3y = x and x + y = 8.

Answer 1

Given linear equation are
y = x (i)
3y = x (ii)
x + y = 8 (iii)
and
for equation y = x
if x = 1, then y = 1
if x = 0, then y = 0
if x = 2, then y = 2
table for line y = x,
$\begin{array}{cccc}X& 0& 1& 2\\ Y& 0& 1& 2\\ Points& 0& A& B\end{array}$
For equation x = 3y
If x = 0, then y = 0, if x = 3, then y = 1 and if x = 6, then y = 2
Table for line x = 3y,
$\begin{array}{cccc}X& 0& 3& 6\\ Y& 0& 1& 2\\ Points& 0& C& D\end{array}$

Plotting the points A(1,1) and B (2,2), we get the straight line AB, plotting the points C (3, 1) and D (6, 2), we get the straight line CD Plotting the points P (0, 8) Q(4, 4) and R (8, 0), we get the straight line PQR. We see that lines AB and CD intersecting the line PR on Q and D respectively.
So, $\Delta$ OQD is formed by these lines. Hence, the vertices of the $\Delta$ OQD formed by the given lines are o(0, 0), Q (4, 4) and D (6, 2)