AlgebraLab

Algebra I Recipe: The Distance and Midpoint Formulas

By G Redden

A. Distance Formula – used to find the distance between any two points.
  1. Use
  2. Label the ordered pairs.
  3. Substitute the values into the formula.
  4. Use order of operations to simplify.

Directions and/or Common Information:

Find the distance between:
(4, 5) & (-2, 6)
(-14, -4) & (1, 8)
(-2, 10) & (5, -3)
B. How to Determine if Three Given Points are the Vertices of a Right Triangle
  1. Label the points using A, B, and C.

  2. Find the 3 lengths (AB, AC, BC) between the points using the distance formula.

    • If the lengths cannot be square rooted evenly, leave in radical form.

  3. Apply the Pythagorean Theorem (a2 + b2 = c2)

    • Substitute the two shortest lengths for "a" and "b".
    • Substitute the longest length for "c".
    • Simplify the equation.
    • If the result is true, the three points make a right triangle.
    • If the result is false, the three points do not make a right triangle.

Directions and/or Common Information:

Determine if the 3 given points would make a right triangle.
(9, 5), (-1, 1), (1, -4)
(-7, -5), (7, 1), (-3, 5)
(1, 4), (-3, -4), (4, 9)
C. Midpoint Formula – used to find the middle of a segment that connects two points.
  1. Use mp =
  2. Label the ordered pairs (x1, y1) and (x2, y2).
  3. Substitute the values into the formula.
  4. Use order of operations to simplify.

Directions and/or Common Information:

Find the midpoint of the segment connecting the following points.
(4, 5) & (-2, 6)
(-14, -4) & (1, 8)
(-2, 10) & (5, -3)

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