Question

A vertex of square is at(1,1) and its two parallel sides are y=x and y=x+1. find the equation of the remaining sides.Show your work;
note:
[ans:x+y=2,x+y=1 or x+y=2 ,x+y=3]
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Answer 1

Answer:

$\displaystyle y = - x + 2$

$y = - x +1$

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

$\displaystyle m_{ \rm perpedicular} = - 1$

since we are given a vertex the equation of the perpendicular line should be

$\displaystyle y - 1 = - 1(x - 1)$

distribute:

$\displaystyle y - 1 = - x + 1$

add 1 to both sides:

$\displaystyle y = - x + 2$

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:

$y - 0.5 = - 1(x - 0.5)$

distribute:

$y - 0.5 = - x +0 .5$

add 0.5 to both sides:

$y = - x +1$

and we are done!