9514 1404 393
Answer:
7.2
Step-by-step explanation:
The problem statement tells you to use the distance formula to find the distance between points A and B. In order to do that, you need to read their coordinates from the graph. You find A(-5, 5) and B(1, 1).
The distance formula is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the point coordinates, the formula tells us the distance is ...
d = √((1-(-5))² +(1-5)²) = √(6² +(-4)²)
d = √(36 +16) = √52 ≈ 7.2111
Rounding the distance to the nearest tenth, we have ...
length AB ≈ 7.2 units
_____
About the Pythagorean theorem
If you draw point C(-5, 1) on the graph, then you can see that triangle ABC is a right triangle. It has legs AC and BC. You can subtract coordinates or count grid squares to see that the lengths of those legs are AC = 4, BC = 6.
The Pythagorean theorem tells you the square of the hypotenuse (AB) is the sum of the squares of the sides (AC and BC).
AB² = 4² +6² = 16 +36 = 52
AB = √52 . . . . as above
