Question

Given a point P(8,1) on segment AB with A(-2,3), find the coordinates of B if ap/ab=2/3. The answer should be entered in the form (x,y) without any spaces between characters

Answer 1

The coordinates of point B are (23,-2)

Explanation:

Mathematically, what this question is telling us is that the point P divides the segment AB in the ratio 2:3

We are now tasked with finding the coordinates of point B

For point P to have divided the segment in that particular ratio, then, internal division formula would have been used.

Mathematically, the internal division formula is given as;

(x,y) = (mx2 + nx1)/(m + n) , (my2 + ny1)/(m + n)

In this particular question case;

(x,y) are coordinates of p = (8,1)

x = 8 , y = 1

m = 2 , n = 3

x1 = -2 , y1 = 3

x2 = x , y2 = y ( coordinates of point B)

So let’s make the substitution;

(8,1) = 2x + 3(-2)/2+3) , 2(y) + 3(3)/(2+3)

(8,1) = (2x-6)/5 , (2y + 9)/5

So therefore; let’s equate

(2x-6)/5 = 8

and 2y+ 9/5 = 1

2x-6/5 = 8

2x -6 = 8*5

2x -6 = 40

2x = 40 + 6

2x = 46

x = 46/2

x = 23

(2y + 9)/5 = 1

2y + 9 = 5 * 1

2y + 9 = 5

2y = 5-9

2y = -4

y = -4/2

y = -2

So the coordinates of point B are (23,-2)