Maths-
General
Easy

Question

Determine whether 𝐴𝐵 and 𝐶𝐷 are congruent. 𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).

hintHint:

      Distance between two points having coordinates (x
1
      , y
1
      ) and (x
2
      , y
2
    ) is given by formula:
    • Distance
    • AB and CD are congruent when AB = CD

The correct answer is: AB and CD are congruent.


    Step by step explanation:
      • Given:
    𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).
    • Step 1:
    • Find AB:

    Distance =  square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root

    therefore AB =square root of left parenthesis negative 2 minus 3 right parenthesis squared plus left parenthesis 4 minus 4 right parenthesis squared end root

    AB =  square root of left parenthesis negative 5 right parenthesis squared plus left parenthesis 0 right parenthesis squared end root

    AB =  square root of 25 plus 0 end root

    AB =  equals square root of 25

    AB = 5
    AB = 5 units.

    • Step 2:
    • Find CD:

    Distance =  square root of open parentheses straight x subscript 2 minus straight x subscript 1 close parentheses squared plus open parentheses straight y subscript 2 minus straight y subscript 1 close parentheses squared end root

    therefore CD =equals square root of left parenthesis 1 minus 1 right parenthesis squared plus left parenthesis 2 minus left parenthesis negative 3 right parenthesis right parenthesis squared end root

    CD =  square root of left parenthesis 0 right parenthesis squared plus left parenthesis 2 plus 3 right parenthesis squared end root

    CD =  square root of 0 plus 25 end root

    CD =  square root of 25

    CD = 5
    CD = 5 units.
    It is clear that,
    AB = CD
    Hence, AB and CD are congruent.