Question

Determine graphically the vertices of the triangle formed by the lines: x–y=0,x-3y=0​

Answer 1

Answer: (0 , 0) ; (4 , 4) ; (6 , 2)

Step-by-step explanation:

Okay, first of all, the question is missing a piece of information as it is impossible to create a triangle using two lines. I searched up online and the other line given is 'x + y = 8'.

The Graphical Method is below in the image. I used an online graphing calculator called 'Desmos. It is convenient to use when you are too lazy to draw graphs manually or are in a hurry.

Manual Method (No Graph):

The vertices of the triangle are nothing but the points of intersection for the lines given but taking two at a time.

1. Let's first take the lines: x – y = 0 & x - 3y = 0​

Let, the point of intersection for the two lines be C. (It doesn't matter what variable you call it. It shouldn't be called x or y, that's it.)

2. Subtract 'x - 3y = 0​' from 'x – y = 0'

x – y = 0

- x + 3y = 0 [Minus(-) * Minus(-) = Plus(+)] => The xs cancel out.

2y = 0

Therefore, y = 0.

3. Now if we put 'y = 0' back into the 'x – y = 0' equation, we can see that x - 0 = 0. So, x = 0.

Therefore, our first coordinate or vertex is (0,0).

4. Let's now take the lines: x – y = 0 & x + y = 8

Let, the point of intersection for the two lines be D. (It doesn't matter what variable you call it. It shouldn't be called x or y, that's it.)

5. Subtract 'x + y = 8​' from 'x – y = 0'

x – y = 0

x + y = 8 => The xs cancel out.

2x = 8

x = 8/2

Therefore, x = 4.

6. Now if we put 'y = 0' back into the 'x – y = 0' equation, we can see that 4 - y = 0. So, y = 4.

Therefore, our second coordinate or vertex is (4,4).

7. Let's take the lines: x + y = 8 & x - 3y = 0​

Let, the point of intersection for the two lines be E. (It doesn't matter what variable you call it. It shouldn't be called x or y, that's it.)

8. Subtract 'x - 3y = 0​' from 'x + y = 8'

x + y = 8

- x + 3y = 0 [Minus(-) * Minus(-) = Plus(+)] => The xs cancel out.

4y = 8

y = 8/4

Therefore, y = 2.

9. Now if we put 'y = 2' back into the 'x - 3y = 0​' equation, we can see that x - 3(2) = 0. So, x - 6 = 0. So, x = 6.

Therefore, our third coordinate or vertex is (6,2)

Therefore, the coordinates or vertices of the triangle are (0,0), (4,4), and (6,2).