Question

The vertices of a triangle are the intersections of the lines whose equations are y = 0, x = 3y, and 3x + y = 7. This triangle is

• A. isosceles
• B. equilateral
• C. right
• D. acute
• E. obtuse

Answer 1

The correct option is C right

• The lines are $y=0$ , $x=3y$ , $3x+y=7$
• The points are $(0,0)$ , $(7/3,0)$ and $(21/10,7/10)$
• The lengths of sides are $7/3$ , $\sqrt{490}/10$ and $\frac{7}{3\sqrt{10}}$
• Observe that ${\left(\sqrt{\frac{490}{100}}\right)}^2+{\left(\frac{7}{3\sqrt{10}}\right)}^2=\frac{490}{100}+\frac{49}{90}=\frac{49}{9}={\left(\frac{7}{3}\right)}^2$
• Therefore it forms a right angles triangle