Mid Point Formula

Q. Question 6
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Q. Question 7
Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Q. In what ratio does the point $(\frac{24}{11},y)$ divide the line segment joining the points P (2, -2) and Q(3, 7)? Also find the value of y.

Q.

Find the coordinates of the centroid of a triangle whose vertices are (0, 6), (8, 12) and (8, 0).

Q.

The midpoint of line segment AB is $(2,-5)$. If the coordinates of point A are $(4,4)$, what are the coordinates of B?

1. $(0,-14)$

2. $(3,\frac{9}{2})$

3. $(0,14)$

4. $(3,-\frac{9}{2})$

Q. Find the ratio in which the point (2, y) divides the line segment joining the points A (−2, 2) and B (3, 7). Also, find the value of y.

Q. Find the midpoint of the line segment joining the points A(-2, 8) and B(-6, -4). [1 MARK]

Q.

If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y) then the relation between x and y can be best described by

1. 6x + y = 8

2. 2x - 5y = 4

3. 3x - y = 5

4. 2x + 1 = 0

Q.

The mid-point of the line segment joining P(-2, 8) and Q(-6, -4) is

1. (-4, -2)

2. (4, 2)

3. (-4, 2)

4. (4, -2)

Q.

In what ratio is the line segment joining (-1, 3) and (4, -7) divided at the point (2, -3)?

1. 2:3

2. 3:5

3. 5:3

4. 3:2

Q.

Find the midpoint of the line segment joining the points A(12, 8) and B(4, 6).

1. (8, 5)

2. (1, 8)

3. (8, 7)

4. (5, 4)

Q. Find the coordinates of the point which divides the line segment joining (−1, 3) and (4, −7) internally in the ratio 3 : 4

Q.

The line segment joining A(-2, 9), and B(6, 3) is a diameter of a circle with centre C. The co-ordinates of C are

1. (0, 0)
2. (2, 6)
3. (2, 0)
4. (1, 1)

Q. Find the points of trisection of the line segment joining the points:

(a) 5, −6 and (−7, 5),

(b) (3, −2) and (−3, −4),

(c) (2, −2) and (−7, 4).

Q. If $P\left(\frac{a}{2},4\right)$ is the midpoint of the line segment joining the points A(−6, 5) and B(−2, 3) then the value of a is [CBSE 2011]
(a) −8 (b) 3 (c) −4 (d) 4

Q. Question 3
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs $\frac{1}{4}$th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Q.

Find the coordinates of the points which divide the line segment joining A (− 2, 2) and B (2, 8) into four equal parts.

Q. Question 1
Determine the ratio in which a line 2x + y – 4 = 0 divides another line segment joining points A(2, – 2) and B(3, 7).

Q. Question 4
If the points A(1, -2) B(2, 3), C(a, 2) and D(-4, -3) from a parallelogram, then find the value of a and height of the parallelogram taking AB as base.

Q.

AB is a diameter of a circle, where A(-3, -4) and B(3, 4). Find its centre and length of diameter.

1. $\begin{array}{c}centre=(0,0)\\ radius=10cm\end{array}$

2. $\begin{array}{c}centre=(5,5)\\ radius=8cm\end{array}$

3. $\begin{array}{c}centre=(0,4)\\ radius=19cm\end{array}$

4. $\begin{array}{c}centre=(-8,4)\\ radius=20cm\end{array}$

Q.

The Point A(2, -3) is reflected in the x axis onto the point A'.Then the point A' is reflected in the line x=4 onto the point A''.

1)Write the coordinates of A' and A''

2)Find the ratio in which the line segment AA'' is divided by the x-axis.Also Find the coordinates of the point of division.

Q.

Find the ratio in which the midpoint of A(12, 8) and B(4, 6) divides the points of trisection of the line AB.

1. $\frac{1}{1}$

2. $\frac{2}{1}$

3. $\frac{1}{2}$

4. $\frac{2}{3}$

Q.

The mid-point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Then the values of a and b are _________ .

1. a = 2, b = 3

2. a = 3, b = 2

3. a = 4, b = 3

4. a = 3, b = 4

Q. Find the point (x, y) that divides the join of A(3, 6) and B(7, 10) in the ratio 3:1

1. (8, 9).
2. (4, 5)
3. (6, 9)
4. None of these

Q.

If the coordinates of the mid-point of the line segment joining the points (2, 1) and (1, -3) is (x, y). What is the relation between x and y?

1. 2x + 1 = 0

2. 6x + y = 8

3. 3x - y = 5

4. 2x - 5y = 4

Q. The midpoint of the line segment joining the points (2, 4) and (10, 12) is .

1. (7, 7)
2. (6, 8)
3. (6, 6)
4. (5, 8)

Q.

In the figure, the mid-points of the sides of the large quadrilateral are joined to draw the small quadrilateral inside. Then the coordinates of points $P$ and $Q$ respectively are

1. $(4,1)$ and $(6,4)$

2. $(6,4)$ and $(4,1)$

3. $(4,2)$ and $(2,4)$

4. $(2,4)$ and $(4,2)$

Q. A point P divides the line segment joining the points A(3, −5) and B(−4, 8) such that $\frac{\mathrm{AP}}{\mathrm{PB}}=\frac{k}{1}.$ If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

Q.

The mid-point of the line segment joining $(2a,4)$ and $(-2,2b)$ is $(1,2a+1)$. Then the values of $a$ and $b$ respectively are

1. 3 and 5

2. 2 and 3

3. 4 and 5

4. 1 and 2

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

1. $y=-9$
2. Both $\left(a\right)$ and $\left(b\right)$
3. $y=3$
4. $y=9$