Everything you're posting involves right triangles, and
each one is solved with the Pythagorean formula:
(one leg)² + (other leg)² = (hypotenuse)²
For the tree . . .
Do you see the right triangle ?
They even marked a little box at the base of the stump
to remind you that there's a right angle there.
-- The stump is 3 meters high.
-- The broken part of the tree is on the ground
13 meters away from the stump.
-- The broken part of the tree is the hypotenuse.
(3)² + (13)² = (broken part)²
-- Before it fell over, the broken part stood on top of the 3-meter stump.
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#4). Your coordinates for point 'G' are correct, but
the coordinates of point 'F' should be (-1, 6), not (1,6).
If you know how to calculate the distance between 2 points,
then that little correction might fix the problem you're having.
The distance between two points is
Square root of [ (x₁-x₂)² + (y₁-y₂)² ]
or
Square root of [ (difference of the x's)² + (difference of the y's)² ] .
Without even using this formula, you could just look at
the graph, and do something like this:
-- From 'F', draw a line 2 units straight down.
-- From 'G', draw a line 4 units to the left.
-- Connect 'F' and 'G' .
Now you have a little right triangle.
The legs are 2 units and 4 units.
The hypotenuse is the distance between 'F' and 'G'.
(2)² + (4)² = (that distance)²