Answer:[tex](x_1,y_1)=(1,-2)[/tex]
[tex](x_2,y_2)=(-8,-2)[/tex]
Step-by-step explanation:
Given
Co ordinates of vertices(1,-6) and (-8,-6)
When two points is given then Length of two points is given by
[tex]L=\sqrt{\left ( x_2-x_1\right )^2+\left ( y_2-y_1\right )^2}[/tex]
[tex]L=\sqrt{\left ( 1-\left ( -8\right )\right )^2+\left ( -6+6\right )^2}[/tex]
[tex]L=\sqrt{9^2}=9 units[/tex]
Perimeter of rectangle is =26 units
Let the other side be x
thus
[tex]2\left ( x+9\right )=26[/tex]
x+9=13
x=4 units
therefore to get the other two co ordinates
such that the length of that side is 4 units is
[tex](x_1,y_1)=(1,-2)[/tex]
[tex](x_2,y_2)=(-8,-2)[/tex]
Horizontal distance will remain same only vertical distance will change in given co ordinates to obtain the remaining two co ordinates
To verify the above two distance between two points must be 13 units
