Answer:
[tex] \displaystyle y = - x + 2[/tex]
[tex]y = - x +1[/tex]
Step-by-step explanation:
we are given a vertex of a square i.e (1,1)
and the equations of the two parallel sides
notice that, the given vertex coordinates satisfy one of the parallel side i.e y=x which means that (1,1) points lie on one of Parallel sides
remember that,
every angles of a square is 90°
therefore,
we need to figure out the remaining Perpendicular line of the given Parallel sides so
let's figure out the perpendicular line of y=x line
recall that,
Parallel lines have the same slope thus
[tex] \displaystyle m_{ \rm perpedicular} = - 1[/tex]
since we are given a vertex the equation of the perpendicular line should be
[tex] \displaystyle y - 1 = - 1(x - 1)[/tex]
distribute:
[tex] \displaystyle y - 1 = - x + 1[/tex]
add 1 to both sides:
[tex] \displaystyle y = - x + 2[/tex]
to figure out the second perpendicular line we can consider the coordinates (0.5,0.5) of y=x equation
so the slope of the perpendicular line is -1
and the equation:
[tex]y - 0.5 = - 1(x - 0.5)[/tex]
distribute:
[tex]y - 0.5 = - x +0 .5[/tex]
add 0.5 to both sides:
[tex]y = - x +1[/tex]
and we are done!
