Question

If A(4, -1), B(5, 3), C(2, y) and D(1, 1) are the vertices of a parallelogram ABCD, find y.​
please complete ans bta chu. ti. ya panti na kae

Answer 1

Answer:

y = 5

Step-by-step explanation:

AB = √[(4-5)²+(-1-3)²] = √[-1²+ -4²] = √1+16 =√17

BC = √[(5-2)²+(3-y)²] = √[3²+3²-6y+y²] = √[9+9-6y+y²] = √[y²-6y+18]

CD = √[(2-1)²+ (y-1)²]  = √[1²+y²-2y+1] = √[y²-2y+2]

AD = √[(4-1)²+(-1-1)²]   = √[3²+ -2²] = √[9+4] = √13

AB = CD and  BC = AD

           CD = AB

√[y²-2y+2] = √17

squaring both sides,

   y²-2y+2 = 17

   y²-2y     = 15

   y²          = 15+2y.....(1)

          BC  = AD

√[y²-6y+18]= √13

squaring both sides,

  y²-6y+18 = 13

  y²-6y      = -5

  y²           = -5+6y......(2)

combining(1) and(2)

      15+2y = -5+6y

     2y-6y  = -5-15

        -4y   = -20

           y   = -20/-4

                = 5