Multiple choice Questions
Q1: Find the centroid of the triangle XYZ whose vertices are X (3,  5) Y ( 3, 4) and Z (9,  2).
(a) (0, 0)
(b) (3, 1)
(c) (2, 3)
(d) (3,1)
Ans: (d)
Centroid of the triangle is given by
Q2: If the midpoint of the line segment joining the points A (3, 4) and B (a, 4) is P (x, y) and x + y  20 = 0, then find the value of a
(a) 0
(b) 1
(c) 40
(d) 45
Ans: (d)
mid point (3+a)/2, 4
Now
(3+a)/2 4 20 = 0
3 + a = 48
a = 45
Q3: Determine the ratio in which the line 2x + y  4 = 0 divides the line segment joining the points A (2,  2) and B (3, 7).
(a) 2:9
(b) 1:9
(c)1:2
(d) 2:3
Ans: (a)
Short Answer type
Q4: The coordinates of one end point of a diameter of a circle are (4, 1) and the coordinates of the centre of the circle are (1, 3). Find the co ordinates of the other end of the diameter.
Ans:
Q5: If the mid point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.
Ans:
Long Answer Type
Q6: Find the centre of the circle passing through (6, 6), (3, 7) and (3, 3)
Ans:
Q7: Prove that the points (3, 0), (4, 5), (1, 4) and (2, 1), taken in order, form a rhombus. Also, find its area.
Ans: The given points are P(3, 0), Q(4, 5), R(1, 4) and S(2, 1).We have
Therefore Sides are equal
PQ = QR = RS = SP = √26
and Diagonal are not equal
PR ≠ QS
Hence PQRS is a rhombus but not a square.
Now Area of rhombus PQRS is given by
A = 1/2 D_{1} × D_{2}
Where D_{1} and D_{2} are diagonals
So
A = 1/2 4√2 × 6√2 = 24sq.units
Q8: Two opposite vertices of a square are (1, 2) and (3, 2). Find the coordinates of other two vertices.
Ans: Let ABCD is the square and A (1,2) and C(3,2). Lets us assume the coordinate of B(x,y)
Now Sides are equal in square, Therefore
AB = BC
Putting the value of x from (1), we get
[(1 + 1)^{2} + (y − 2)^{2}] = 8
Solving it ,we get
y^{2} − 4 y = 0
Solving this quadratic equation, we get y = 0 or 4
So coordinates of the other vertices are (1, 0) and (1, 4)
Q9: Find a point on y  axis which is equidistant from the points (5, 2) and (3, 2).
Ans: Let the point on y axis is P(0,y) which is equidistant from the points A(5,2) and B(3,2). Then
PA = PB
Q10: If the coordinates of the mid points of the sides of a triangle are (1, 2), (0, 1) and (2, 1). Find the coordinates of its vertices.
Ans:
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