Math, asked by vamsikrishnamonapat5, 9 months ago

find the fourth vertix of the parallelogram whose consecutive vertices are(8,4),(5,7),(-1,1)​

Answers

Answered by Rythm14
37

Let the vertices be,

  • A(8,4)
  • B(5,7)
  • C(-1,1)
  • D(x,y)

In a parallelogram, diagonals bisect each other.

•°• Midpoint of AC = Midpoint of BD

--------------------------------------------------------

We know that, Midpoint formula =

( \frac{ {x}_{1}  +  {x}_{2} }{2} ,\frac{ {y}_{1}  +  {y}_{2} }{2})

-------------------------------------------------------

Now,

 \rightarrow \: ( \frac{ {8 + ( - 1)}}{2} , \frac{ {4 + 1}}{2} ) = ( \frac{ {5 + x}}{2} , \frac{ {7 + y}}{2} ) \\  \rightarrow \: ( \frac{ {8   - 1}}{2} , \frac{ {5}}{2} ) = ( \frac{ {5 + x }}{2} , \frac{ {7 + y}}{2} ) \\  \rightarrow \: ( \frac{ {7}}{2} , \frac{ {5}}{2} ) = ( \frac{ {5 + x }}{2} , \frac{ {7 + y}}{2} ) \\  \underline{equating \: x \: and \: y \: coordinates \colon} \\ \rightarrow \frac{7}{2 }  =  \frac{5 + x}{2} \\ \rightarrow \: 7 = 5 + x \\ \rightarrow \: 7 - 5 = x \\ \rightarrow \: 2 = x \\  \therefore \: x \:  = 2 \\  \underline{also \colon} \\ \rightarrow \:  \frac{5}{2}  =  \frac{7 + y}{2}  \\ \rightarrow \: 5 = 7 + y \\ \rightarrow \: 5 - 7 = y \\ \rightarrow - 2 = y \\  \therefore \: y \:  =  - 2

____________________________

(x,y) = (2,-2)

•°• The fourth vertice is, (2,-2).

Answered by MarshmellowGirl
12

 \large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}

Attachments:
Similar questions