Answer:
Step-by-step explanation:
You want the lengths of segments n and p in the graphs shown.
Pythagorean theorem
You can consider each segment to be the hypotenuse of a right triangle. The lengths of the legs of that triangle can be found by counting the grid squares in the vertical and horizontal directions.
For hypotenuse c and legs 'a' and 'b', the Pythagorean theorem tells you ...
c² = a² +b²
c = √(a² +b²)
3. Segment n
n = √(3² +1²) = √(9 +1)
n = √10
4. Segment p
p = √(4² +3²) = √(16 +9) = √25
p = 5
