Let’s practice using the distance formula.

A calculator, paper, and pencil are needed.

D = √(xx − x1)2 + (y2 − y1)2

If we have two points, say (3, -4) and (-8, 5), how do they fit into the Distance Formula?

Well, we have two points; one is the (x1,y1) point and the other is the (x2,y2) point. One way to keep track of which point is which is to write on top of the points with a different color pencil or pen as in the example below:

(x1, y1) (3, -4)     (x2, y2) (-8, 5)

Next, we re-write the Distance Formula and substitute in the point values.

D = √(-8 − 3)2 + (5 − -4)2

Last, simplify the equation following all the order of operation rules.

D = √(-8 − 3)2 + (5 − -4)2

D = √(-8 − 3)2 + (5 + 4)2

D = √(-11)2 + (9)2

D = √121 + 81

D = √202

D ≈ 14.2       approximate answer due to rounding

Let’s practice using the distance formula.

D = √(xx − x1)2 + (y2 − y1)2

Practice using the distance formula by solving the problems below.

  1. What is the approximate distance between points (-4, 9) and (-12, 8)?
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    ≈ 8.1 Close Pop Up
  2. What is the approximate length of WZ when the coordinates of its endpoints are (3, -8) and (-2, -5)?
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    ≈ 5.8 Close Pop Up
  3. What is the approximate distance between points (-5.2, 6.2) and (-6.2, 7.2)?
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    ≈ 1.4 Close Pop Up
  4. What is the distance between ( 5 over 6 5 6 , -2) and (3, - 1 over 3 1 3 )?
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    2.73
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  5. Find the side lengths of triangle UVW, with vertices U(1, -6), V(1, 3), and W(-1, 5) Is triangle UVW an isosceles triangle? How can you tell?
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    Check Your Answer

    No, because the side lengths are all different:
    UV = √81 = 9, VW = √8 ≈ 2.8, and UW = √125 ≈ 11.2 Close Pop Up
  6. If parallelogram ABCD has vertices at A( 3, 6), B(9, 13), C(3,-1) and D(9,6). Verify that opposite sides have equal lengths.
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    Check Your Answer

    AB = √85 ≈ 9.2 opposite to CD = √85 ≈ 9.2
    BD = √49 = 7 opposite to AC = √49 = 7
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