Coordinate Geometry

Q. The area of a triangle is 5. Two of its vertices are (2, 1) and (3, -2). The third vertex is (x, y) where y = x + 3. Then the co-ordinate of the third vertex is

1. $(\frac{7}{2},\frac{13}{2})or(-\frac{3}{2},\frac{3}{2})$
2. $(\frac{-7}{2},\frac{13}{2})or(\frac{3}{2},\frac{3}{2})$
3. $(\frac{1}{2},\frac{3}{2})$
4. $(\frac{3.}{2},\frac{1}{2})$

Q. If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5), then the centroid of the triangle is:

1. (5/3, 2)
2. (5/6, 1)
3. (2, 5/3)
4. (1, 5/6)

Q. The points (p - 1, p+2), (p, p+1), (p+1, p) are collinear for

1. p = 0
2. p = 1
3. p = - 1 / 2
4. Any value of p

Q. Orthocentre of the triangle whose sides are given by 4x - 7y + 10 = 0, x + y - 5 = 0 & 7x + 4y - 15 = 0 is

1. (1, - 2)
2. (-1, -2)
3. (-1, 2)
4. (1, 2)

Q. A square lawn has a circular pond in the centre. Find the shaded region's area given that the diameter of circle is $\frac{1}{3}$ times the diagonal of square with sides 3 cm.

1. $\frac{9-\pi }{2}$
2. $\frac{(18-\pi )}{4}$
3. $\frac{(18-\pi )}{18}$
4. $\frac{(2+\pi )}{8}$

Q. Find the area of $\Delta PCD$, P lies on the line AB, where O is the centre of the outer circle with radius 6.5 cm. ABCD is a rectangle, one of its sides is 5 cm.

1. $30c{m}^2$
2. $45c{m}^2$
3. $36c{m}^2$
4. $50c{m}^2$

Q. The coordinates of the diagonals of a square are (2, 0) and (0, 5). What is the area of the square?

1. $\frac{\sqrt{29}}{\sqrt{2}}sq.units$
2. $29sq.units$
3. $\frac{29}{4}sq.units$
4. $14.5sq.units$

Q. Point of intersection of the diagonals of square is at origin and coordinate axis are drawn along the diagonals. If the side is of length a, then one which is not the vertex of square is:

1. $(0,\frac{a}{\sqrt{2}})$
2. $(\frac{a}{\sqrt{2}},0)$
3. $(a\sqrt{2},0)$
4. $(-\frac{a}{\sqrt{2}},0)$

Q. One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its vertices are (-3, 1) and (1, 1). Which of the following is not an equation of the other three straight lines?

1. 14x - 8y = 6
2. 7x - 4y = - 25
3. 4x + 7y = 11
4. 14x - 8y = 20

Q. Which one of the following points on the line 2x - 3y = 5 is equidistant from (1, 2) and (3, 4)?

1. (7, 3)
2. (4, 1)
3. (1, -1)
4. (-2, -3)