Answer:
1) (4,6),(-4,6), (4,12),(-4,12)
2) (4,9) or (-4,9)
Step-by-step explanation:
Observe that the two vertices given, (0,6) and (0,12) are on the y-axis.
The distance between this points is |12-6|=6
We know area of a triangle is [tex]A=\frac{1}{2}bh[/tex]
We were given area as 12.
[tex]\frac{1}{2}*b*6=12[/tex]
[tex]3b=12[/tex]
b=4 units
We can find a point 4 units horizontally away from any of the vertex.
So (4,6),(-4,6), (4,12),(-4,12) are feasible vertices.
For the triangle to be isosceles, then the third vertex must be on the horizontal line through the midpoint of (0,6) and (0,12) and must be 4 units away from the line x=0.
Therefore if thr triangle is isosceles, then third vertex must be at (4,9) or (-4,9)
