Question

E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis .Find the coordinates of H and G. Please need answer quick with accurate explanation.​

Answer 1

coordinates of H = (1, 0)

Coordinates of G = ( - 3.6, -2) or (5.6, -2)

Explanation:

E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis.

Let the coordinates of H is (x, 0) and G is (a, b).

The length of side EF is

`EF = √((5 -2)^2 + (3 +1)^2) = 5`

So,

`EH = √((5 -x)^2 + (3 -0)^2) = 5\\\\(5 -x)^2+ 9 = 25\\\\5 - x = 4\\\\x = 1`

And

`GH = √((a -x)^2+ b^2) = 5\\\\(a -1)^2+ b^2 = 25\\\\a^2 + b^2 + 1 - 2 a = 25\\\\a^2 + b^2 - 2a = 24 .... (1)`

Now

`FG = √((a -2)^2+ (b +1)^2) = 5\\\\(a -2)^2+ (b+1)^2 = 25\\\\a^2 + b^2 + 2b - 2 a = 20\\ ..... (2)`

Solving (1) and (2)

b = - 2 ,

`a = (2 \pm√(4 + 80))/(2)\\\\a = (2 \pm 9.2)/(2)\\\\a = - 3.6, 5.6`