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Determine the length of the line segment shown. line segment from negative 2 comma 2 to 2 comma negative 1

User Rida
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1 Answer

1 vote

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.

Determine the length of the line segment shown. line segment from negative 2 comma-example-1
User ShawnOrr
by
7.8k points

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