On one straight line at an equal distance from each other on one side of the road there are three telegraph poles.

On one straight line at an equal distance from each other on one side of the road there are three telegraph poles. The outermost ones are at distances of 1.5 m and 7.5 m from the road. Find the distance at which the middle post is from the road.

The described arrangement of the three telegraph poles and the road is a trapezoid. A trapezoid is a quadrangle whose opposite sides are parallel. One of the bases of the trapezoid will be equal to the distance from the road to the first telegraph pole, we will designate it as “a”. The other base of the trapezoid will be equal to the distance from the road to the second telegraph pole, denote it “b”. Then, in accordance with the condition of the problem, a = 1.5 m., B = 7.5 m.
Since all three pillars are on one straight line at an equal distance from each other, then the distance at which the middle pillar is located is equal to the midline of the trapezoid. The middle line of the trapezoid is the segment connecting the midpoints of the sides of the trapezoid. The middle line of the trapezoid is found by the formula:
c = (a + b) / 2
Substitute the corresponding values ​​into the formula:
c = (1.5 + 7.5) / 2 = 9/2 = 4.5 (m.)
Answer: 4.5 m.