Math Problem Statement

distance between the pair of points (10, 8) and (14,5)

Solution

To find the distance between the two points (10,8)(10, 8) and (14,5)(14, 5), we can use the distance formula:

Distance=(x2x1)2+(y2y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Here, (x1,y1)=(10,8)(x_1, y_1) = (10, 8) and (x2,y2)=(14,5)(x_2, y_2) = (14, 5).

Substituting the values into the formula:

Distance=(1410)2+(58)2\text{Distance} = \sqrt{(14 - 10)^2 + (5 - 8)^2}

Distance=(4)2+(3)2\text{Distance} = \sqrt{(4)^2 + (-3)^2}

Distance=16+9\text{Distance} = \sqrt{16 + 9}

Distance=25\text{Distance} = \sqrt{25}

Distance=5\text{Distance} = 5

So, the distance between the points (10,8)(10, 8) and (14,5)(14, 5) is 5 units.

Would you like more details or have any questions?

Here are some related questions:

  1. How do you find the midpoint between two points?
  2. What is the slope of the line passing through these two points?
  3. How can you determine if two points are equidistant from a third point?
  4. How does the distance formula relate to the Pythagorean theorem?
  5. What is the equation of the line passing through these two points?

Tip: When using the distance formula, ensure you correctly identify and subtract the corresponding coordinates to avoid sign errors.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Distance Formula

Formulas

Distance formula

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 7-9