Coordinate geometry of 2 dimensions

1. If the three vertices of a rectangle taken in order are the points
(2, -2), (8, 4) and (5, 7), the coordinates of the fourth vertex are
a. (1, 1)
b. (1, -1)
c. (-1, 1)
d. None of these

Answer-c. (-1, 1)

2. If the vertices of a triangle have integral coordinates, then the triangle is
a. Equilateral
b. Never equilateral
c. Always isoceles
d. None of these

Solution- An irrational number can't be equal to a rational number.
Hence a triangle with coordinates of the vertices as integers can't be
an equilateral triangle.

Answer- b. Never equilateral