Mid Point

Q.

At what time (approx) between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together?

1. 8 : 03

2. 8 : 37

3. 8 : 11

4. 8 : 46

Q.

What are the coordinates of the origin?

Q.

What is the relation between n (A), n( B), n(A intersection B)

and n(A union B)

Q.

If two adjacent vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals intersect at (2, -5) then find the coordinates of the other two vertices.

Q.

If $\sqrt{3}\sin \theta =\cos \theta$, find the value of $\frac{3{\cos }^2\theta +2\cos \theta }{3\cos \theta +2}$

Q.

A, B, C, D, E, F, G and H are sitting around a circle facing at the centre. B is second to the right of H and third to the left of A. D is not an immediate neighbour of either B or H and is second to the right of F. C is fourth to the right of G.

Who is third to the right of E?

1. Data inadequate

2. None of these

3. F

4. C

Q.

Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units

Q. Question 13
If $P(\frac{a}{3},4)$ is mid-point of the line segment joining points Q(-6, 5) and R(-2, 3), then value of a is
(A) – 4
(B) – 12
(C) 12
(D) – 6

Q.

Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the line joining of the middle points of its diagonals meet in a point and bisect one another.

Q. ABCD is a parallelogram. The coordinates of A, B and C are (4, 5), (–2, 3) and (–3, –5), then the coordinates of D are

1. (-3, 3)
2. (3, -5)
3. (3, -3)
4. (5, -3)

Q.

What is corollary?

Q.

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are

(a) (-6, 7) (b) (6, -7) (c) (4, 2) (d) (5, 3)

Q. If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.

Q.

ABCD is a parallelogram with vertices A (X₁, Y₁) , B(X₂, Y₂) and C (X₃, Y₃). Then the coordinates of the fourth vertex D in terms of the coordinates of A, B and C are

1. X₁ + X₃ - X₂, Y₁ + Y₃ - Y₂

2. X₁ - X₂ - X₃, Y₁ - Y₂ - Y₃

3. X₁ + X₂ + X₃, Y₁ + Y₂ + Y₃

4. X₁ + X₂ - X₃, Y₁ + Y₂ - Y₃

Q.

If three consecutive vertices of a parallelogram ABCD areA(1, -2), B(3, 6) and C(5, 10), find its fourth vertex D.

Q.

If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is

(a) 3 (b) 4 (c) 0 (d) $\frac{3}{2}$

Q.

If R (5, 6) is the mid-point of the line segment AB joining the points A (6, 5) and B (4, y), then y equals

(a) 5 (b) 7 (c) 12 (d) 6

Q.

The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

Q.

Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex.

Q.

If the complex numbers $z_1,z_2,z_3$represent the vertices of an equilateral triangle such that $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|$, then $z_1+z_2+z_3$equal:

1. $0$

2. $1$

3. $-1$

4. None of these

Q. The mid-point of the line segment joining the points A(–2, 6) and B(–3, –4) is

1. (-5, 5)
2. $(\frac{5}{2},-5)$
3. (-1, -2)
4. $(\frac{-5}{2},1)$

Q.

The coordinates of the point P are (-3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Q. The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.

Q.

The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.

Q.

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of $△ABC$ and AD is a median, then the coordinates of D are

(a) $(\frac{5}{2},3)$ (b) $(5,\frac{7}{2})$ (c) $(\frac{7}{2},\frac{9}{2})$ (d) none of these

Q.

$\frac{[2\sin \theta \tan \theta (1-\tan \theta )+2\sin \theta se{c}^2\theta ]}{{(1+\tan \theta )}^2}$

1. $\frac{\sin \theta }{(1+\tan \theta )}$

2. $\frac{2\sin \theta }{(1+\tan \theta )}$

3. $\frac{2\sin \theta }{{(1+\tan \theta )}^2}$

4. $Noneofthese$

Q.

If P(-1, 1) is the midpoint of the line segment joining A(-3, b) and B(1, b+4) then b=?

(a) 1 (b) -1 (c) 2 (d) 0

Q.

If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Q.

$ABCD$ is a rectangle and $P,Q,R$ and $S$ are mid-points of the sides $AB,BC,CD$ and $DA$ respectively. Show that the quadrilateral $PQRS$ is a rhombus.

Q. The midpoint of line segment joining A(2, 3) and B(4, 5) lies on the curve.

1. $x+y=5$
2. $x^2+y^2=25$
3. $x+2y=8$