Question

Draw the graphs of the equations $x-y+1=0$ and $3x+2y-12=0$. Determine the co-ordinates of the vertices of the triangle formed by these lines and the $x$-axis, and shade the triangular region.

• A. $A(1,3),B(-1,6)$ and $C(4,0)$
• B. $A(2,5),B(-1,6)$ and $C(2,0)$
• C. $A(-2,5),B(-1,6)$ and $C(2,0)$
• D. $A(2,3),B(-1,0)$ and $C(4,0)$

Answer 1

The correct option is D $A(2,3),B(-1,0)$ and $C(4,0)$

For equation $x–y+1=0$ or $x=y-1$, we have following points which lie on the line

Plug $y=0,1$ we get

$x=0-1=-1$

$x=1-1=0$

Therefore, the required points are $(-1,0),(0,1)$.

For equation $3x+2y–12=0$ or $y=\frac{12-3x}{2}$, we have following points which lie on the line

Plug $x=0,4$ we get

$y=\frac{12-0}{2}=6$

$y=\frac{12-12}{2}=0$

Therefore, the required points are $(0,6),(4,0)$.

We can see from the graphs that points of intersection of the lines with the x–axis are $(–1,0),(2,3)$ and $(4,0)$.