Answer:
Q2. (16,8)
Q3.
, ratio=5:1
Q4. Ratio=2:1
Q5. Ratio=1:1
Step-by-step explanation:
Q2. Let (2a,a) be the coordinates of P.
Since P is equidistant from Q (2,-5) and R (-3, 6), we have

This gives us:


Expand:



The coordinates of P are 
Q.3 The equation of the line segment joining the points
A (5.-6) and B (-1,-4) is
.
The x-coordinate of the point that divides AB in the ratio m:n is

The y-axis meets this line at 
We substitute
into this equation and solve for m and n.



Therefore the ratio is m:n=5:1
Q.4 The equation of the line segment joining
the points (-5,-4) and (-2,3) is
.
The point (-3, k) must satisfy this line because it lies on it.
.

We again use the equation
to find the given ratio.
Substitute: 



The ratio is m:n=2:1
Q. 5 The equation of the line joining A (2,3) and B(6,-3) is
.
We substitute (4,m) to get:
12+4m=12
4m=0
m=0
It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).
Hence the ratio is 1:1