Maths-
General
Easy

Question

Compare the distance AB with AC.

hintHint:

Distance between two points having coordinates (x1, y1) and (x2, y2) is given by formula:
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

The correct answer is: 1.13 units.


    • Step by step explanation:
    ○        Given:
    Points A (5,6), B (11,10) and C(11, 5).
    ○        Step 1:
    ○        Find distance between AB
    ○        A (5,6) and B (11,10)
    ○     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
    Distance = square root of left parenthesis 11 minus 5 right parenthesis squared plus left parenthesis 10 minus 6 right parenthesis squared end root
    rightwards double arrowDistance = square root of left parenthesis 6 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root
    rightwards double arrowDistance = equals square root of 36 plus 16 end root
    rightwards double arrowDistance = square root of 52
    rightwards double arrowDistance = 7.21 units
    ○        Step 1:
    ○        Find distance between AC
    ○        A (5,6) and C (11,5)
    ○     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
    Distance = square root of left parenthesis 11 minus 5 right parenthesis squared plus left parenthesis 5 minus 6 right parenthesis squared end root
    rightwards double arrowDistance = square root of left parenthesis 6 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root
    rightwards double arrowDistance = square root of 36 plus left parenthesis 1 right parenthesis end root
    rightwards double arrowDistance = square root of 37
    rightwards double arrowDistance = 6.08 units
    ○        Step 1:
    ○        Difference  between AB and AC
    rightwards double arrow7.21 - 6.08
    rightwards double arrow1.13 units
    ●       Final Answer:
    Hence, AB is longer than AC by 1.13 units.

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