Answer with Step-by-step explanation:
We are given that
Equation of line segment SP =[tex]y=2x+3[/tex]
We have to find the equations of the line segments forming the 3 other sides of a rectangle.
Substitute the x=0 in given equation
Then, we get
[tex]y=3[/tex]
Substitute y=0 then, we get
[tex]0=2x+3[/tex]
[tex]2x=-3[/tex]
[tex]x=-\frac{3}{2}=-1.5[/tex]
Hence, the equation of line segment SP passing from the point (0,3) and (-1.5,0).
By comparing withe y=mx+c
We get m=2=Slope of line segment SP
The line segment SR is perpendicular to the line segment SP and passing form the point (-1.5,0).
Slope of line segment SR=[tex]\frac{-1}{Slope\;of\;SP}=-\frac{1}{2}[/tex]
Because when two lines are perpendicular then the relation between the slopes of two lines is given by
[tex]m_2=-\frac{1}{m_1}[/tex]
The equation of line segment of SR is given by
[tex]y=m(x-x_1)+y_1[/tex]
The equation of line segment SR with slope -1/2 and passing from the point (-1.5,0) is given by
[tex]y=-\frac{1}{2}(x+1.5)[/tex]
[tex]y=-\frac{1}{2}x-0.75[/tex]
Line segment RQ is parallel to SP
So,Slope of line RQ=2
Because when two lines are parallel then their slope are equal.
Line segment PQ is perpendicular to SP
Therefore, slope of PQ=[tex]-\frac{1}{2}[/tex]
The equation of line segment PQ with slope -1/2 and passing through the point (0,3) is given by
[tex]y=-\frac{1}{2}(x-0)+3[/tex]
[tex]y=-\frac{1}{2}x+3[/tex]
Substitute x=0 in [tex]y=-\frac{1}{2}x-0.75[/tex]
Then, we get y=-0.75
The equation of line segment RQ with slope 2 parallel to SP and passing through the point (0,-0.75)is given by
[tex]y=2x-0.75[/tex]
