Given the three vertices F(-5, 0), G(3, -3), and H(-2, 8), what are the coordinates of I that make quadrilateral FGIH a square?

Question

Given the three vertices F(−5, 0), G(3, −3), and H(−2, 8), what are the coordinates of I that make quadrilateral FGIH a square?

Answer 1

Hello Hannah,

 

In a square, the diagonals intersect. The midpoints of both diagonals are the same point.

 

Find the midpoint for the diagonal HG.

 

H (-2,8) and G (3, -3)

 

Midpoint formula: 

 

 ( (x₁ + x₂₎ / 2 , (y₁ + y₂) / 2)  

 

The midpoint is the average, so..  Add the x values and divide by 2, then add the y values and divide by 2. Create an ordered pair.

 

Therefore the midpoint for HG is (1/2, 5/2).

 

The midpoint of the other diagonal FI is also (1/2, 5/2). Use this information to solve for the coordinates of point I.

 

F ( -5, 0) and I (x,y).

 

First let's find x. Add the x values and divide by 2. Set this equal to the x coordinate for the midpoint of HG, which is 1/2.

 

Like this:

 

(x - 5) / 2 = 1/2 

 

Cross multiply and set the products equal to each other. 

 

2x - 10 = 2

2x = 12

x = 6

 

Do the same for y.

 

(y + 0) = 5/2

 

Cross multiply and set the products equal to each other.

 

2y = 10

y = 5

 

The coordinates of point I which make FGIH a square are (6,5).

 

I hope this helps!