Answer:
(c) 5 units
Step-by-step explanation:
The distance between two points can be found using the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((1 -(-3))² +(-1 -2)²) = √(4² +(-3)²) = √(16 +9) = √25
d = 5
The distance between the two points is 5 units.
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Additional comments
If you draw a right triangle using the grid lines and the straight line between the two points, you find that the leg lengths are 3 and 4. These tell you the right triangle is a 3-4-5 right triangle, so the hypotenuse (distance between the points) is 5 units.
These numbers, {3, 4, 5}, are known as a "Pythagorean triple" because they are integers that satisfy the Pythagorean theorem relating sides of a right triangle. Several other such triples often seen in algebra and trig problems are {5, 12, 13}, {7, 24, 25}, {9, 40, 41}, {8, 15, 17}.
The {3, 4, 5} triple is the smallest set of integers that are a Pythagorean triple. It, and multiples of it, are also the only ones in which the differences are the same (the sequence is arithmetic).
