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Answer:
The co-ordinates are O(0,0) A(-3,5) B(5,3) and C (2.2,8)
Step-by-step explanation:
Given:
One vertex of square on origin and other end at (-3,5)
And perimeter of square=20
To Find:
Select all the coordinates of the missing vertices.
Solution:
Given co-ordinate forms one length of square
(Refer the attachment)
and we know that all sides of square are equal and makes 90 degree angle
So,
Perimeter=4*side of square
Here Side of square= Distance from origin to (-3,5)
Using distance formula=Sqrt[(0+3)^2+(0-5)^2]
=Sqrt(9+25)
=Sqrt(34)
=5.831 units
So the length of side=5.831 units
So from (-3,5) to other co-ordinate distance will remain the same i.e. 5.831
Using Geometry, as a symmetry length will remain same for square
So, other co-ordinate will be (5,3) in 1st quadrant.
Now drawing the length=5.831 at 90 angle from co-ordinate (-3,5) and (5,3)
we get the following point as ,
Point will represent the diagonal for the square ,
Distance of diagonal =length*sqrt(2)=5.831*1.414=8.2 units......equation(1)
The point is obtaining x=2.2 and y=8
So to check distance of diagonal from origin it should equal to length of diagonal.
so Distance formula from origin to (2.2,8) is
=Sqrt[(0-2.2)^2+(0-8)^2]
=Sqrt[(68.84)]
=8.2 .........Equation(2)
Hence comparing equation(1) and (2) we get ,
That the Co-ordinate for square are correct as follows, named as OABC
O(0,0) A(-3,5) B(5,3) and C (2.2,8)
