Answer:
5
Explanation:
You want the length of the line segment between (-2, 2) and (2, -1).
Pythagorean theorem
The relation between the side lengths of a right triangle is given by the Pythagorean theorem. It tells you ...
c² = a² +b²
where c is the hypotenuse of the triangle, and 'a' and 'b' are the legs.
Leg lengths
When you plot the points on a grid, you can identify the vertical and horizontal distances between them by counting grid squares, or by finding the difference of coordinates:
AB = B -A = (2, -1) -(-2, 2) = (2 +2, -2 -2) = (4, -3)
The point on the right is 4 horizontal units and 3 vertical units from the point on the left.
Segment length
The above relation tells us the segment length is ...
c² = 4² +3² = 16 +9 = 25
c = √25 = 5
The length of the line segment is 5 units.
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Additional comment
The integer triple of segment lengths that form a right triangle is called a "Pythagorean triple." The one relevant to this problem is {3, 4, 5}. Others often seen in algebra, trig, and geometry problems are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
and multiples of these. If you become familiar with these triples, you can often write down the answer to a question like this simply by recognizing the dimensions involved.