Question

y, axis divides the line segment joining
(1, 4) and (-3,5)in the ratio​

Answer 1

Answer: Ratio = 9 : 1

Step-by-step explanation:

First, write the equation of line joining the points (-3,5) & (1,4)

Slope (m) = (4 - 5)/(1+3) = -1/4

Line : (y - 4) = (-1/4) (x - 1)

Line : x + 4y = 17 _________ ( I )

Now, if y-axis cuts the Line.

So, put x = 0 in ( I )

On putting x = 0 we get y = 17/4

Line intersect the y-axis at (0, 17/4)

So, finally calculate the distance between (-3,5) to (0, 17/4) &

(0, 17/4) to (1,4)

And then divide them.

Let distance between (-3,5) & (0, 17/4) is d1 and between (0, 17/4) & (1,4) is d2.

From distance formula

d1 = √( (-3)^2 + (3/4)^2 ) = 153/16

d2 = √( (1)^2 + (-1/4)^2 ) = 17/16

Finally, d1/d2 = (153/16)/(17/16) = 153/17

d1/d2 = 9/1

Hence, 9 : 1 _________(Ans.)

Hope it helps ^_^