Consider a line equidistant from and parallel to both lines that contain the bases of a trapezoid.
y=2x+1
Practice makes perfect
The equations of two parallel lines which contain the bases of a trapezoid are given in the exercise. Let's first draw their graphs.
The exercise wants us to find the equation of the line that contains the midsegment of the trapezoid. To find it we will recall the properties of the midsegment of a trapezoid.
A midsegment of a trapezoid is parallel to the bases of a trapezoid.
A midsegment of a trapezoid is equidistant from the bases of a trapezoid.
The equations of the lines are in slope-intercept form. Thus, we can observe that their slopes are 2.
y= 2x+7
y= 2x-5
Since the parallel lines have the same slope, the slope of the midsegment line will be 2 as well. With this information we can partially write the equation of the midsegment line.
y= 2x+b
From here we will find the value of b, which is the y-intercept of the line. To do so, since the midsegment line is equidistant from the base lines, we will find the midpoint of the y-intercepts of them using the Midpoint Formula. Note that the y-intercepts of the lines are (0,7) and (0,-5).
M(+/2,7+(-5)/2) → M(0,1)
Therefore, the y-intercept of the midsegment line is at M(0,1). Finally, we can complete the equation as follows.
y=2x+1
