the endpoints of a line segment pq are p(-8,-5)and q(7,7).point r lies on the ling segment pq and divids it in two line segments such that the ratio of pr to pq is 5:1.

Answer 1

p = (-8, -5) and q = (7, 7)

And if pq/pr = 5:1 (instead of 1:5 which is not possible when r is between p and q)

the x-coordinate changes by 15 (from –8 to 7) going from p to q

the x-coordinate changes by 12 (from –5 to 7) going from p to q

Going from p to r the x and y coordinates will shange by 1/5 these amounts.

So the x-coordinate of r will be –8 + 15/5 = –8 + 3 = –5

and the y-coordinate of r will be –5 + 12/5 = –5 + 2.4 = –2.6

Answer

r = (-5, -2.6)

Answer 2

Vectors pq = <15, 12>. If r = <x, y> then vector pr = <x + 8, y + 5>. pr = 5/6pq, <x + 8, y + 5> = 5/6<15, 12> =

<12.5, 10>, x + 8 = 12.5; x = 4.5; y + 5 = 10; y = 5.

Answer: r = (4.5, 5)