But they are just lines!

Geometry Level 2

{ x + y = 0 3 x + y 4 = 0 x + 3 y 4 = 0 \large \begin{cases}{ x + y = 0 } \\ {3x + y - 4 = 0 } \\ {x + 3y - 4= 0 } \end{cases}

The intersection points of these straight lines form a triangle. What kind of triangle is this?

None of these Equilateral Isosceles Right Angled

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2 solutions

Ryoha Mitsuya
Jun 15, 2015

We get (2,-2) and (-2,2) as the intersection resulting from solving for x and y using Linear Systems. The last two equations are inverse functions of each other, meaning that both lines are reflections of each other over the line x=y. Thus the triangle is Isosceles because both (2,-2) and (-2,2) are equidistant from x=y. Also an equilateral triangle is a type of an Isosceles triangle so putting it as an option is weird. If you want to, you can calculate the third point by using the fact that x=y to be sure as well, which leads to (1,1)

Rwit Panda
Jun 12, 2015

Finding the intersection points of these 3 lines we get them as (1,1), (2,-2), and (-2,2). The distance of (2,-2) and (-2,2) from (1,1) is same, i.e. sqrt(10). So it is isosceles.

Or could also be called the Martix of a problem .

Alissa Yandell - 5 years, 12 months ago

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