External Division

Q.

The coordinates of the mid-point of the line segment joining two points P(X₁, y₁, z₁) and Q(x₂, y₂, z₂) are:

1. 

2. 

3. 

4. 

Q. If D E F are the midpoints of the triangle ABC are (x1, y1) ( x2, y2) and (x3, y3) then find the coordinates of its vertices.

Q.

The coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are given by

1. 

2. 

3. 

4. 

Q. 15. Find the acute angle between the lines l1 and l2 where l1 is formed by joining the points (0, 0) and (2, 3) and l2 by joining points (2, -2) and (3, 5)

Q. The harmonic conjugate of the point $R(2,4)$ with respect to the points $P(2,2)$ and $Q(2,5)$ is

1. $(2,4)$
2. $(2,8)$
3. $(4,2)$
4. $(4,8)$

Q.

A point R with x-coordinate 1 lies on the line segment joining the points P(-2, 3, 5) and Q (7, 0, -1). The coordinates of the point R are

1. (1, -2, 3)

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

3. (-1, 2, 3)

4. (1, 2, 3)

Q. The coordinates of the point(s) which divide(s) the line segment joining the point $(5,-2)$ and $(9,6)$ in the ratio $3:1,$ are

1. $(11,10)$
2. $(8,4)$
3. $(10,11)$
4. $(4,8)$

Q. If $H$ is the harmonic mean between $P$ and $Q$ then the value of $\frac{H}{P}+\frac{H}{Q}$ is

1. $2$
2. $\frac{PQ}{P+Q}$
3. $\frac{P+Q}{PQ}$
4. $\frac{1}{2}$