Mid Point

Q. Points X, Y, Z are collinear such that d(X, Y) = 17, d(Y, Z) = 8, find d(X, Z) .

Q. 35. Find the equation of circle passing through (3, 4)(3, 2)and(1, 4)

Q. Find the points which divide the line segment joining $A(-11,4)$ and $B(9,8)$ into four equal parts.

Q.

The points $z_1,z_2,z_3,z_4$ in the complex plane are the vertices of a parallelogram taken in order if and only if

1. $z_1+z_4=z_2+z_3$

2. $z_1+z_3=z_2+z_4$

3. $z_1+z_2=z_3+z_4$

4. $Noneofthese$

Q. Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.

Q. 9. Find the equation of the circle passing through the point (2, -6) (-3, 1) & (6, 4)

Q.

In the given figure, D and E are mid points of sides AB and AC of $△$ABC. Which of the following is true ?

1. $DE=\frac{1}{2}BC$, by mid point theorem

2. ​$DE=\frac{1}{2}BC$ , by converse of mid point theorem

3. $DE=\frac{1}{2}AB$, by mid point theorem

4. $DE=\frac{1}{2}AB$, by converse of mid point theorem

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

Q. 38. Equation of the circle on the line joining the points (1, -3) and (2, 5) as diameter is

Q. 29 Let ABC be a triangle with AB=AC.if D is mid point of BC, E the foot of perpendicular drawn from D to AC and F the mid point DE then prove that AF is perpendicular to BE.

Q. Three vertices of a parallelogram $\text{ABCD}$ taken in order are $\text{A}(3,6)$, $\text{B}(5,10)$ and $\text{C}(3,2)$ find :
(i) the coordinates of the fourth vertex $\text{D}$.
(ii) length of diagonal $\text{BD}$.

Q.

In the given figure, D and E are mid points of sides AB and AC of $△$ABC. Which of the following is true ?

1. $DE=\frac{1}{2}BC$, by mid point theorem

2. ​$DE=\frac{1}{2}BC$ , by converse of mid point theorem

3. $DE=\frac{1}{2}AB$, by mid point theorem

4. $DE=\frac{1}{2}AB$, by converse of mid point theorem

Q. 18. Find the orthocenter of the triangle formed by the coordinate axes and + y = 4

Q.

In the given figure, D and E are mid points of sides AB and AC of $△$ABC. Which of the following is true ?

1. $DE=\frac{1}{2}BC$, by mid point theorem

2. ​$DE=\frac{1}{2}BC$ , by converse of mid point theorem

3. $DE=\frac{1}{2}AB$, by mid point theorem

4. $DE=\frac{1}{2}AB$, by converse of mid point theorem

Q. Draw the graph for each equation given below; hence find the intercepts on the co-ordinate axes: $\frac{1}{3}x+\frac{1}{5}y=1$

1. $(9,0),(0,2)$
2. $(6,0),(0,8)$
3. $(3,0),(0,5)$
4. $(2,0),(0,6)$

Q. Find the coordinates of the point P which divides line segment QR internally in the ratio m:n in the following examples
(i) Q $\equiv$(-5, 8) R$\equiv$(4, -4) and m:n = 2:1

Q. ABC and ABD are two triangle on the same base AB .if line segment CD is bisected by AB at O show that ar(ABC)=ar(ABD)

Q. Draw the graph for each equation given below; hence find the co-ordinates of the points where the graph drawn meets the co-ordinate axes:
$\frac{2x+15}{3}=y-1$.

Q. Prove that every line segment has one and only one mid-point.​

Q. The points $A(1,-2),B(2,3),C(k,2)$ and $D(-4,-3)$ are the vertices of a parallelogram. Find the value of $k$.

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

Q. Show that the points $(3,-2),(4,0),(6,-3)$ and $(5,-5)$ are the vertices of a parallelogram.

Q. The co-ordinates of □EFGH are E(3, −2), F(7, −2), G(5, −5) and H(1, −5) respectively. Draw □EFGH and state its type.