In what ratio does(-5,-6) divide the line segment joining (-9,-10) and (7,6)? What formula will you use?

Question

Answer 1:3

Answer 1

First, I think, you need to calculate the slope of the segment that you say...

This calculates to 1. So you need to connect the point (-5, -6) with a line of slope -1, to make it perpendicular. But since, with a little calculation, the point (-5, -6) is already on the line segment, then just use one of the coordinates to solve it. Let's use x in this case.

(-9 - (-5)) / (-9 - (+7)) = 1/4, so the ratio is 1:3.

Answer 2

Yes, compare the difference of coordinates. Either x-coordinates or y-coordinates. They are to be taken in order. Say the given two points the line segment be A and B and the point dividing the line segment AB be P. Then the order of points is A P B or B P A.
A(x1,y1)
B(x2,y2)
P(x,y)
The ratio=(x1-x):(x-x2) or (y1-y):(y-y2)
Here, the ratio=-9-(-5):-5-7=-4:-12=1:3 (taking x-coordinates)
ans=1:3
But you please find the ration taking the y-coordinates as well. The ratio must be the same in both cases. If the ratio is not same then the point P does not belong to the line containing A and B.

Answer 3

I will compare the difference of their x-coordinates.
(-5)-(-9)=4
7-(-5)=12
4:12=1:3
This is the fastest way.

Answer 4

using

D = sqrt((x2 - x1)^2 + (y2 - y1)^2))

You will get 1:3

(-9,-10) and (-5,-6) = 4sqrt(2)
(7,6) and (-5,-6) = 12sqrt(2)

(4sqrt(2))/(12sqrt(2)) = 1 : 3

I would had showed you better, but since i had already answered this before, i shortened it.

Answer 5

i guess distance formula