Question

The point P(x,y) is 4/5 of the way from the point A(8, -1) to the point B(-2, 4). Find the ordinate of point P.

Answer 1

Let (x,y) divide the line joining points A(8,-1) and B(-2,4) in the ratio m1 and m2

x = (x1m2 + x2m1)/ (m1+m2)

y = (y1m2 + y2m1)/ (m1 + m2)

And as this point 4/5 of the way

It means it is as a distance of 4 from point A

So, m1 = 4 and m2 = 1

x = ((8x1) + (-2x4))/ ((4+1))

x = (8-8)/ 5

x = 0

And y = ((4x4)+(-1x1))/(4+1)

y = (16-1)/5

y = 3

hence, co ordinate of point P is (0,3) -------Answer

Another method

Total distance between x co ordinate of line AB

= 10 units

So, 4/5 of the way means

= 4x 10/5 = 8 units from point A

So x co ordinate becomes ( as it is decreasing from 8 to -2) 0

Total distance between y co ordinate between point A and B

= 4+1 = 5 units

As this point is 4/5 on the way from A to B

= 4x5/5 = 4 units

But as y is increasing

So y co- ordinate becomes ( -1 +4 ) = 3

( As it is increasing)

So co ordinate of point P becomes ( 0,3) so ordinate is 3

i have solved the problem by two methods, whichever is easy for you ...you can use.

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