A triangle is drawn using the lines y = x, x = -2, and y = 4. Work out the coordinates of the three vertices of the triangle.

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).