Midpoint Formula

Q.

The coordinate of the mid-point of the line segment joining the points (2, 1) and (1, -3) is ____.

1. $(-3,-2)$

2. $(3,-2)$

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

4. $(4,-1)$

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

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

Q. Question 3 (iii)
The points $A(x_1,y_1),B(x_2,y_2)andC(x_3,y_3)$ are the vertices of $\Delta$ ABC.
Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

Q.

$ABCD$ is a rectangle formed by the points $A(-1,-1)$ , $B(-1,4)$ , $C(5,4)$ and$D(5,-1)$ . $P,Q,R$ and $S$ are the midpoints of $AB,BC,CD$ and $DA$ respectively. Is the quadrilateral $PQRS$ a square? a rectangle? or a rhombus? Justify your answer.

Q.

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

1. (1, - 12), (5, - 10)

2. (1, - 10), (5, - 12)

3. (2, - 10), (5, - 12)

4. (1, - 10), (2, - 12)

Q. Match the following with the midpoints of the line segment joining the given two points.

1. $\left(\frac{7}{2},\frac{9}{2}\right)$
2. $\left(\frac{9}{2},5\right)$
3. $\left(\frac{13}{2},\frac{11}{2}\right)$
4. $\left(2,5\right)$

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

Q. The foot of the perpendicular from the point $(1,6,3)$ to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

1. $(1,3,5)$
2. $(-1,-1,-1)$
3. $(2,5,8)$
4. $(-2,-3,-4)$
5. $(\frac{1}{2},2,\frac{1}{2})$

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. If the point $(x_1+t(x_2-x_1),y_1+t(y_2-y_1\left)\right)$ divides the join of $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $t:1-t$, then

1. $t<0$
2. $0<t<1$
3. $t=1$
4. $t>1$

Q.

Midpoint of the line joining the points ($x_1,y_1$) and ($x_2,y_2$) is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

1. True

2. False

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 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. $A(2,5),B(-1,2)$ and $C(5,8)$ are the vertices of a triangle ABC, 'M' is a point on AB such that AM $:$ MB $=1:2$. Find the co-ordinates of 'M'. Hence find the equation of the line passing through the points C and M.

Q.

A(3, 0) is the midpoint of the line joining P(3, 3) and Q(3, -3).

1. True

2. False

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 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. 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. 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

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. Find the perpendicular distance of the point $(1,0,0)$ from the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+0}{8}$. Also, find the coordinates of the foot of perpendicular.

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.

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.

A(3, 0) is the midpoint of the line joining P(3, 3) and Q(3, -3).

1. True

2. False

Q. Find the coordinates of the points which divide the line segment joining the points $(-4,0)$ and $(0,6)$ in $4$ equal parts.

1. $\left(\begin{array}{c}-3,\frac{3}{2}\end{array}\right)$
2. $(-2,3)$,
3. $\left(\begin{array}{c}-1,\frac{9}{2}\end{array}\right)$
4. All of the above