The tops of seven water fountains in the Italian City of Reggio Emilia form a straight line. The first fountain is 120cm and the last one is 12cm. How tall is the third water fountain from the left?

I have absolutely no idea, please help!!!

Use Cartesian geometry

let the first be at (1,120) and the last one at (7,12)
slope = (120-12)/(1-7) = -18

so for each increase in x, the height drops 18 cm
so you want two decreases,
height of third = 120-2(18) = 84

or
find the equation:
y = -18x + b
at (7,12)
12 = -18(7) + b
b = 138

y = -18x + 138
so when x = 3
y = -18(3) + 138 = 84 cm

or

the fountains would be at
(1,120) , (2, 102) , (3,84) , (4,66) , (5,48) , (6, 30), (7, 12)

Thank you

To find the height of the third water fountain from the left, we need to determine the difference in height between each fountain.

First, we calculate the total difference in height between the first and the last fountain:

Total Difference = Height of Last Fountain - Height of First Fountain
= 12 cm - 120 cm
= -108 cm

Since the total difference is negative, it means that the height is decreasing as we move from the first fountain to the last fountain.

Next, we need to find the incremental difference in height between each fountain.

Incremental Difference = Total Difference / (Number of Fountains - 1)
= -108 cm / (7 - 1)
= -108 cm / 6
= -18 cm

Now that we know the incremental difference, we can determine the height of the third water fountain from the left.

Height of Third Fountain = Height of First Fountain + (Incremental Difference * (Number of Fountains from the Left - 1))
= 120 cm + (-18 cm * (3 - 1))
= 120 cm + (-18 cm * 2)
= 120 cm + (-36 cm)
= 120 cm - 36 cm
= 84 cm

Therefore, the height of the third water fountain from the left is 84 cm.