Question

Find the coordinates of the vertices of a square inscribed in the triangle with vertices A(0,0), B(2,1), C(3,0); given that two of its vertices are on the side AC.

Answer 1

We can see that AC is x axis.
Let the vertices of the square be:  (a, 0),  (a, b), (a+b, b) and (a+b, b)

Equation AB:  y =  x/2        as A(0,0) and B=(2,1)
Since  (a,b) lies on it:     b = a/2  

Equation of BC:  y + x = 3    as A(2,1)  B(3,0)
Since   (a+b, b)  lies on it,      a+b+b = 3 

Solving the two equations    b = 3/4     and  a = 3/2

Hence coordinates are:  (3/2,0)  (3/2, 3/4),  (9/4, 3/4) , (9/4, 0)

Answer 2

Answer:

Step-by-step explanation:

We can see that AC is x axis.

Let the vertices of the square be:  (a, 0),  (a, b), (a+b, b) and (a+b, b)

Equation AB:  y =  x/2        as A(0,0) and B=(2,1)

Since  (a,b) lies on it:     b = a/2  

Equation of BC:  y + x = 3    as A(2,1)  B(3,0)

Since   (a+b, b)  lies on it,      a+b+b = 3 

Solving the two equations    b = 3/4     and  a = 3/2

Hence coordinates are:  (3/2,0)  (3/2, 3/4),  (9/4, 3/4) , (9/4, 0

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