9. If the coordinates of midpoints of sides of triangle are (1,2), (0-1) and (2,-1), find the co-ordinates of the vertices​

Question

9. If the coordinates of midpoints of sides of triangle
are (1,2), (0-1) and (2,-1), find the co-ordinates of
the vertices​

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Serenity 1 month 2021-08-12T20:13:14+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-12T20:15:03+00:00

    Answer:

    Let A(x

    1

    y

    1

    ),B(x

    2

    ,y

    2

    )andC(x

    3

    ,y

    3

    ) be the vertices of △ABC.

    Let D(1,2) ,E(0,-1) and F(2,-1) be the mid -points of sides BC,AC and AB

    Since D is the mid point of BC.

    A(x

    1

    y

    1

    ),B(x

    2

    ,y

    2

    )andC(x

    3

    ,y

    3

    )

    2

    x

    2

    +x

    3

    =1and

    2

    y

    2

    +y

    3

    =2

    ⟹x

    2

    +x

    3

    =2y

    2

    +y

    3

    =4→ (i)

    Similarly , E and F are the mid-points of CA and Ab respectively

    2

    x

    1

    +x

    3

    =0and

    2

    y

    1

    +y

    3

    =−1

    ⟹x

    1

    +x

    3

    =2andy

    1

    +y

    3

    −2→(2)

    2

    x

    1

    +x

    2

    =2and

    2

    y

    1

    +y

    2

    =−1

    ⟹x

    1

    +x

    2

    =4andy

    1

    +y

    2

    =−2→(3)

    From (1),(2),and(3)

    (x

    2

    +x

    3

    )+(x

    1

    +x

    3

    )+(x

    1

    +x

    2

    )=2+0+4

    (y

    2

    +y

    3

    )+(y

    1

    +y

    3

    )+(y

    1

    +y

    2

    )=4−2−2

    ⟹x

    1

    +x

    2

    +x

    3

    =3andy

    1

    +y

    2

    +y

    3

    =0→(4)

    From (1) and (4)

    x

    1

    +2=3andy

    1

    +4=0

    ⟹x

    1

    =1andy

    1

    =−4∴(1,−4)

    From (2) and (4)

    x

    2

    +0=3andy

    2

    −2=0

    ⟹(x

    2

    ,y

    2

    )=B(3,2)

    From (3) and (4)

    x

    3

    +4=3andy

    3

    −2=0

    ∴(x

    3

    ,y

    3

    )=C(−1,2)

    ∴ Coordinate of △ABC are ⇒ (1,−4);B(3,2);C(−1,2)

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