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.

$b=\dfrac{b_1+b_2}{2}$

$b=\dfrac{7-5}{2}$

$b=\dfrac{2}{2}$

$b=1$

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 $y=2x+1$.