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

Question

answer is 1:3

Answer 1

Here is the working out:

The line segment between (-9,-10) and (7,6) has a length in x of 16 and a length in y of 16. The point (-5,-6) is 4 units along x and 4 units along y, making it 12 units distance in x from the far end, and 12 units distance in y from the far end. The ratio in which the line segment is divided is 4:12 along x, and likewise 4: 12 along y. In lowest terms, the ratio is 1: 3.

Answer 2

First make sure all the points are on the same line:
Yes, they all satisfy the equation Y = X - 1
Distance between points (-9,-10) and (7,6) is:
D^2 = 16^2 + 16^2 (Pythagorian theorum)
Therefore D= 16 * SQRT(2)
Distance between points (-9,-10) and (-5,-6) is:
E^2 = 4 * SQRT(2)
So, one line segment is 1/4 and the other is 3/4 so the ratio between the two line segments is 1:3

Answer 3

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Answer 4

(7,6) and (-5,-6)
D = sqrt((7 - (-5))^2 + (6 - (-6))^2)
D = sqrt((12)^2) + 12^2)
D = sqrt(144 + 144))
D = sqrt(288)
D = 12sqrt(2)

(-9,-10) and (-5,-6)
D = sqrt((-9 - (-5))^2 + (-10 - (-6))^2)
D = sqrt((-4)^2 + (-4)^2)
D = sqrt(16 + 16)
D = sqrt(32)
D = 4sqrt(2)

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

ANS : 1 : 3

Answer 5

(-9,-10) (7,6)
(-5,-6)

(-9-(-5))/(-5-7)= -4/-12=1/3
In general,
If point X,Y divides the line joining (X1,Y1) AND (X2,Y2) in the ratio l:m then,
l/m = (X1-X)/(X-X2) = (Y1-Y)/(Y-Y2).

all the best.