Answer:
6.32 units
Step-by-step explanation:
The line shown can be considered to be the hypotenuse of a right triangle that has side lengths of 2 and 6. These values can be found by counting the vertical and horizontal numbers of grid squares between the two end points.
The Pythagorean theorem is used to find the length of the hypotenuse. It tells you the square of the hypotenuse is equal to the sum of the squares of the sides:
AB² = 2² +6²
AB² = 4 + 36 = 40
Taking the square root, you find ...
AB = √40 ≈ 6.32456
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We want to round this value to the nearest hundredth, so we look at the thousandths digit to see whether to round up. That digit is 4, so we simply delete all the digits to the right of the hundredths place.
Line AB is 6.32 units long.
