Find The Distance Between Two Points Worksheet

6 problems

Finding the distance between two points is a fundamental concept in geometry and algebra. The distance between two points `(x_1, y_1)` and `(x_2, y_2)` can be calculated using the distance formula:

`\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}`

This formula involves subtracting the `x`-coordinates and `y`-coordinates of the two points, squaring the results, adding them together, and then taking the square root of the sum.

Algebra 1
Coordinate Plane

How Will This Worksheet on "Find the Distance Between Two Points" Benefit Your Students' Learning?

  • Reinforces the application of the distance formula.
  • Shows practical applications of distance calculation.
  • Develops problem-solving skills through various exercises.
  • Enhances spatial reasoning abilities.
  • Prepares students for advanced geometry and real-world scenarios.

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Solved Example

Q. Find the distance between the points (9,6)(-9,-6) and (3,2)(-3,2).\newlineRound decimals to the nearest tenth.\newline___\_\_\_ units
  1. Calculate Differences: Calculate the differences in the xx-coordinates and yy-coordinates of the points.x2x1=3(9)=6x_2 - x_1 = -3 - (-9) = 6y2y1=2(6)=8y_2 - y_1 = 2 - (-6) = 8
  2. Use Distance Formula: Use the distance formula: distance=(x2x1)2+(y2y1)2\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. distance=62+82=36+64=100\text{distance} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100}
  3. Calculate Square Root: Calculate the square root of 100100.100=10.0\sqrt{100} = 10.0

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