Midpoint Formula

Q. If 𝑨(−𝟐, 𝟏), 𝑩(𝒂, 𝟎), 𝑪(𝟒, 𝒃) and 𝑫(𝟏, 𝟐) are the vertices of a parallelogram 𝑨𝑩𝑪𝑫, find the values of 𝒂 and 𝒃. Also, find the lengths of its sides.

Q. Find the co-ordinates of the point M if M is the midpoint of a line segment PQ with P(7, -3) and Q(-6, 2).

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

Q. Find the co-ordinates of the point P if P is the midpoint of a line segment AB with A(4, 1) and B(-3, 5).

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

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. $x+2y=8$

Q.
In the given figure, P is the midpoint of AB. Find the value of m.

1. 2
2. -3
3. 3
4. -2

Q. Find the coordinates of the midpoint of the line segment joining the points (2, 1) and (1, -3).

1. $(0,\frac{1}{3})$
2. $(2,\frac{-3}{5})$
3. $(\frac{3}{2},-1)$
4. $(\frac{1}{4},0)$

Q.

A(1, 2), B(4, 6) and C(8, 12) form the vertices of a triangle. Which of the following is not the coordinates of medians of triangle ABC?

1. $(\frac{5}{2},4)$
2. (6, 9)
3. $(\frac{9}{2},7)$
4. $(\frac{7}{2},4)$

Q.

If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram, find the values of a and b.

1. a = 2 and b = 3
2. a = 1 and b = 1
3. a = 1 and b = 4
4. a = 1 and b = 3

Q. If the points A(1, 2), B(4, 3), C(1, 0) and D(p, -1) are the vertices of a parallelogram then, find the value of p.

1. 4
2. 0
3. 3
4. -2

Q. If (7, 3), (6, 1), (8, 2) and (p, q) are the vertices of a parallelogram, taken in order, then the value of p is

1. 9