Find the distance between the points (1, -3) and (-1, 2).
Understand the Problem
The question appears to be asking for the distance between two points in a coordinate system, specifically points (1, -3) and (-1, 2). This involves using the distance formula to calculate the required distance based on their coordinates.
Answer
The distance is \( \sqrt{29} \).
Answer for screen readers
The distance between the points ( (1, -3) ) and ( (-1, 2) ) is ( \sqrt{29} ).
Steps to Solve
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Identify the coordinates The points provided are ( A(1, -3) ) and ( B(-1, 2) ).
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Use the distance formula The distance ( d ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is given by the formula: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
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Substitute the coordinates Substituting the coordinates of the points ( A ) and ( B ): $$ d = \sqrt{((-1) - 1)^2 + (2 - (-3))^2} $$
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Calculate the differences Calculate ( (-1) - 1 = -2 ) and ( 2 - (-3) = 2 + 3 = 5 ).
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Square the differences Now, square these results: $$ d = \sqrt{(-2)^2 + 5^2} $$ This simplifies to: $$ d = \sqrt{4 + 25} $$
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Add the squares Now perform the addition: $$ d = \sqrt{29} $$
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Final result The distance between points ( A(1, -3) ) and ( B(-1, 2) ) is ( \sqrt{29} ).
The distance between the points ( (1, -3) ) and ( (-1, 2) ) is ( \sqrt{29} ).
More Information
The distance formula is fundamental in coordinate geometry, allowing us to calculate the distance between any two points on a Cartesian plane. The result ( \sqrt{29} ) is approximately 5.39 units.
Tips
- Confusing the order of coordinates when substituting into the formula.
- Forgetting to square the differences before summing them.
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