Question

I don't understand this,so can you please explain more clearly. Where did you get the 1/5?

1.The point P divides the interval joining A(-1,-2) to B(9,3) internally in the ratio 4:1. Find the coordinates of P.

Answer 1

(4*9+ 1*-2)/(4+1), (4*3 + 1*-2)/(4+1)
((36-2)/5, (12-2)/5))

(34/5, 10/5)

(34/5, 2) or (6.4, 2)

Answer 2

eh?

since the line is divided into ratio 4:1, you can consider it divided into fifths. P is 4/5 of the way along the line. That means its x-coordinate is 4/5 of the way from -1 to 9, and its y-coordinate is 4/5 of the way from -2 to 3.

The distance from -1 to 9 is 9-(-1) = 10.
4/5 of 10 is 8

Similarly for y, 4/5 of the way from -2 to 3 is 4.

So starting at A, add 8 to x and 4 to y to get

P = (7,2)