Question

help me please

Answer 1

the sides of the triangle at right are formed by the graphs of 3x + 2y = 1, y = x -2, and -4x + 9y = 22. Is the triangle isosceles? How do you know?

Answer 2

well this is a difficult question.

you can

Use some graphing software or a site like

https://www.desmos.com/calculator

to graph the lines.This will help you get an idea of the look of the triangle and then make a decision about the likely sides that could be equal.

1. find the points where each pair of lines intersect...

2. find the distance between any 2 vertices...

and trying to find 2 sides with the same lengths

An alternate method is to find the slope of each line and
then find the angle between 2 lines

If you can show 2 angles are the same then the triangle is isosceles

The formula for the angle between 2 lines is

\[\tan(\theta) = \frac{m_{1} - m_{2}}{1 + m_{1} \times m_{2}} \]

so depending on what you know the choice is yours


Hope it helps