For an isosceles triangle, two sides are equal and for right triangle o angle should be of 90 degree.
Let the third point coordinate be (x,y).
The distane between given point (-2,-4) and (4,-4) is 6.
The on angle is 90 degree which means one side is perependicular to the given side.
The coordinate of third point must be equal to (4,y) or (-2,y).
As triangle is isosceles so distance between point (4,y) and (4,-4) is equal to 6.
[tex]\begin{gathered} 6=\sqrt[]{(4-4)^2+(y+4)^2} \\ 6=(y+4) \\ y=6-4 \\ =2 \end{gathered}[/tex]
Thus coordinate of third point can be (4,2).
Second case if third point is (-2,y).
Distance between point (-2,y) and (-2,-4) is 6, as triangle is isosceles triangle.
[tex]\begin{gathered} 6=\sqrt[]{(-2+2)^2+(y+4)^2} \\ 6=(y+4) \\ y=2 \end{gathered}[/tex]
Thus third coordinate can be (-2,2).
As from the options only (4,2) is correct.
