Question

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Answer 1

Hey there!!

First, the vertices of a triangle are the corners, we can see the vertices if this triangle, this triangle is in the center.

When we take the coordinates, we write it in this form:

(x, y)

The first vertice: the top one

Lying 0 on the x axis and 2 on the y axis (0,2)

The second vertices: to the right

Lying 2 on the x axis and 0 on the y axis (2,0)

The third vertice: to the left

Lying -1 on x axis and -3 on y axis ( -1,-3)

Option (A)

Answer 2

Heya Mate ^^"

(•) There are four lines there and consequently, four points that can make on 4 Possible Triangles ^^

(•) The one hidden line there =_=

$y + 3x = 2$

Hopefully, it's intersections won't help with the desired triangle.
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Now, kept aside the other stuff !

The Triangles would have vertices such that the points will satisfy pair wise the line equations ✓✓

( I ) Solution for :

$y + x = 2 \\ y = 2x - 1$

$(x,y) \equiv (1,1)$

( ii )

$x + y = 2 \\ y = x - 2$

$(x,y) \equiv (2,0)$

( iii )

$y = 2x - 1 \\ y = x - 2$

$(x,y) \equiv ( - 1, - 3)$
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And there you go with the three vertices ^_^

$(x,y) \equiv [(1,1),( - 1, - 3),(2,0)]$