Question

solve this - find the two vertices of that square whose opposite vertices are (1,1) and (1,8) ​

Answer 1

Step-by-step explanation:

We note that the diagonals bisect one another at right angles, so that AO = OC = DO = h2h2.

Since the xx-coordinates of B and D are the same, diagonal BD is parallel to the yy-axis,

and since AC is at right angles to BD, it is parallel to the xx-axis.

This means that the yy-coordinates of A and C are the same.

Clearly h=8−1=7h=8−1=7 so that h2=3.5h2=3.5

Hence the coordinates of C

are (1+3.5,1+3.5)=(4.5,4.5)(1+3.5,1+3.5)=(4.5,4.5)

and the coordinates of A

are (1–3.5,1+3.5)=(−2.5,4.5)