I need help with #4. Please help. I have to show all work so please explain

9514 1404 393

  5

Step-by-step explanation:

Use the distance formula.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((4 -0)²+(3 -0)²) = √(4² +3²) = √(16 +9) = √25

  d = 5

The distance between the two points is 5 units.

Additional comment

The most commonly seen Pythagorean triples are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) and their multiples.

In problem 4, once you see that the differences of the coordinates are 3 and 4, you can consult your memory of the (3, 4, 5) Pythagorean triple to recognize the hypotenuse length of a triangle with sides 3 and 4 is 5.

Similarly, in problem 5, you recognize the coordinate differences as 5 and 12, so you know from the (5, 12, 13) Pythagorean triple that the distance will be 13.