Respuesta :
Given:
The bases of a trapezoid lie on the lines
[tex]y=2x+7[/tex]
[tex]y=2x-5[/tex]
To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
On comparing [tex]y=2x+7[/tex] with slope intercept form, we get
[tex]m_1=2,b_1=7[/tex]
On comparing [tex]y=2x-5[/tex] with slope intercept form, we get
[tex]m_2=2,b_2=-5[/tex]
The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.
[tex]m=m_1=m_2=2[/tex]
The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.
[tex]b=\dfrac{b_1+b_2}{2}[/tex]
[tex]b=\dfrac{7-5}{2}[/tex]
[tex]b=\dfrac{2}{2}[/tex]
[tex]b=1[/tex]
So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get
[tex]y=2x+1[/tex]
Therefore, the equation of line that contains the midsegment of the trapezoid is [tex]y=2x+1[/tex].
