Question

The bases of a trapezoid lie on the lines y=2X +7 and y= 2X -5. Write the equation that contains the midsegment of the trapezoid

Answer 1

Given:

The bases of a trapezoid lie on the lines

`y=2x+7`

`y=2x-5`

To find:

The equation that contains the midsegment of the trapezoid.

Solution:

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

On comparing
`y=2x+7` with slope intercept form, we get

`m_1=2,b_1=7`

On comparing
`y=2x-5` with slope intercept form, we get

`m_2=2,b_2=-5`

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.

`m=m_1=m_2=2`

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.

`b=(b_1+b_2)/(2)`

`b=(7-5)/(2)`

`b=(2)/(2)`

`b=1`

So, the y-intercept of the required line is 1.

Putting m=2 and b=1 in slope intercept form, we get

`y=2x+1`

Therefore, the equation of line that contains the midsegment of the trapezoid is
`y=2x+1`.