Monday

December 22, 2014

December 22, 2014

Posted by **shirsh** on Saturday, December 1, 2012 at 9:12am.

- geometry -
**Reiny**, Saturday, December 1, 2012 at 10:31amthe two diagonals of a square right-bisect each other at the point (2,2) , the midpoint of the given points .

let the other vertex be (x,y) , the endpoint of the other diagonal

since the two diagonals must be perpendiculars, their slopes must be negative reciprocals of each other

(y-2)/x-2) = -(2-0)/(2-1)

(y-2)/(x-2) = -2/1

-2x+4 = y-2

y = 6-2x

we also know that the segments of the diagonals are equal

√((x-2)^2 + (y-2)^2 ) = √((2-0)^2 + (2-1)^2 )

square both sides

(x-2)^2 + (y-2)^2 = 5 , ahhh, the equation of the circumscribed circle

subbing in our y = 6-2x

(x-2)^2 + (4-2x)^2 = 5

x^2 - 4x + 4 + 16 - 16x + 4x^2 - 5 = 0

5x^2 -20x +15 = 0

x^2 - 4x + 3 = 0

(x-1)(x-3) = 0

x = 1 or x = 3

if x = 1 then y = 6-2 = 4 ---> point (1,4)

if x = 3 then y = 6-6 = 0 ---> point (3,0)

I have a feeling there should be an easier way, but I can't see it right now. Sometimes I tend to overthink the question.

**Answer this Question**

**Related Questions**

Algebra - Here is my question: If (2, -3) and (-5, 4 are the endpoints of a ...

math - hi i will ask u in math :) in (( distance between two points )) * three ...

Algebra II-Please check my calculation - Find center, vertices, co-vertices and ...

analytic geometry/graphing problem - The vertices of a triangle are the points ...

7th Grade Geometry - A Rectangle with vertices A B C AND D. The triangle is ...

Algebra 2 - Choose the equation that best represents an ellipse for the given ...

math - A rectangle has one side on the x-axis and two vertices on the curve y=6...

Geometry - Determine whether the polygons with the given vertices are similar. ...

Geometry - Triangle ABC has vertices A = (0,6) B = (-2,3), and C = (2,1). Find ...

Geometry - I need help with vertices! The vertices of triangle FGH are F(1,1), G...