The vertices of the triangle are the points where the lines intersect. We need to find the intersection points for each pair of lines.
1. **Intersection of y = x and x = -2:**
Substitute x = -2 into y = x.
y = -2.
So, the first vertex is **(-2, -2)**.
2. **Intersection of y = x and y = 4:**
Substitute y = 4 into y = x.
4 = x.
So, the second vertex is **(4, 4)**.
3. **Intersection of x = -2 and y = 4:**
These equations directly give the coordinates.
x = -2 and y = 4.
So, the third vertex is **(-2, 4)**.
The three vertices are (-2, -2), (4, 4), and (-2, 4).
The vertices of a shape defined by lines are the points where those lines intersect. We have three lines, so we need to find the intersection points of the three possible pairs of lines.
**Pair 1: Intersection of `y = x` and `x = -2`**
We can solve this by substitution. Since we know `x = -2`, we substitute this value into the first equation:
`y = -2`
So, the first vertex is at the coordinates **(-2, -2)**.
**Pair 2: Intersection of `y = x` and `y = 4`**
Again, we use substitution. We know `y = 4`, so we substitute this into the first equation:
`4 = x`
So, the second vertex is at the coordinates **(4, 4)**.
**Pair 3: Intersection of `x = -2` and `y = 4`**
These equations already give us the x and y coordinates directly.
`x = -2` and `y = 4`
So, the third vertex is at the coordinates **(-2, 4)**.
The three vertices of the triangle are (-2, -2), (4, 4), and (-2, 4).
Expert