Question

Michel is drawing a square with one vertex on the origin (-3, 5) and a perimeter of 20. Select all the coordinates of the missing vertices, not including (-3, 5).

Answer 1

The co-ordinates are O(0,0) A(-3,5) B(5,3) and C (2.2,8)

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)