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.

(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)

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)

To find the coordinates of point P, which divides the interval AB internally in the ratio 4:1, we can use the concept of section formula.

The section formula states that if a line segment is divided by a point (P) in the ratio of m:n, where m and n are positive integers, then the coordinates of P can be determined using the following formula:

Px = (mx2 + nx1) / (m + n)
Py = (my2 + ny1) / (m + n)

In this case, A(-1, -2) represents (x1, y1) and B(9, 3) represents (x2, y2), while the ratio is given as 4:1, which means m = 4 and n = 1.

Now, substituting the given values into the formula:

Px = (4 * 9 + 1 * -1) / (4 + 1)
Px = (36 - 1) / 5
Px = 35 / 5
Px = 7

Py = (4 * 3 + 1 * -2) / (4 + 1)
Py = (12 - 2) / 5
Py = 10 / 5
Py = 2

Therefore, the coordinates of point P are (7, 2).