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If the vertices of a parallelogram …

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If the vertices of a parallelogram PQRS taken in order are P(3,4),Q(-2,3),R(-3,-2), then the coordinates of its fourth vertex S are?
  • 2 answers

Vivek Prajapati 2 years, 3 months ago

Right

Shubh Lakshna Pandey 2 years, 3 months ago

It is given in the question that, The vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2) Let, the fourth vertices is S (x , y). The parallelogram's PQRS's vertices, listed in order. Because of this, a parallelogram's diagonals are split in half. We know that the diagonals of a parallelogram bisects with each other. ∴   Coordinates of the PR's midpoint = coordinates for QS's midpoint (332,422)=(2+x2,3+y2)(0,1)=(2+x2,3+y2)
(23−3​,24−2​)=(2−2+x​,23+y​)(0,1)=(2−2+x​,23+y​)​ Now, 0 = \frac{-2+x}{2}0=2−2+x​ .............(1) Simplify the equation, 0=2+xx=2
0=−2+xx=2​ Again, 1=\frac{3+y}{2}1=23+y​ ...............(2) Simplify the equation, 1=3+y22=3+yy=1
1=23+y​2=3+yy=−1​ the coordinates of its fourth vertex S are (2,-1).
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