Answer:
RP/SP =3 , RP/RS = 3/4
Explanation:
Here is the complete question
Three colinear points on the coordinate plane are R(x,y) S(x+8h, y+8k) and P(x+6h,y+6k) Determine value of RP/SP and RP/RS?
Solution
We first find the length of RS, SP and RP as follows
RS = S(x+8h, y+8k) - R(x,y)
= √[((x + 8h) - x)² + ((y + 8k) - y)²]
= √[x - x + 8h)² + (y - y + 8k)²]
= √[(8h)² + (8k)²] = 8√(h² + k²)
SP = P(x + 6h,y + 6k) - S(x+8h, y+8k)
= √[((x + 6h) - (x + 8h))² + ((y + 6h) - (y + 8k))²]
= √[x - x + 6h - 8h)² + (y - y + 6k - 8k)²]
= √[(-2h)² + (-2k)²] = 2√(h² + k²)
RP = P(x+6h, y+6k) - R(x,y)
= √[((x + 6h) - x)² + ((y + 6k) - y)²]
= √[x - x + 6h)² + (y - y + 6k)²]
= √[(6h)² + (6k)²] = 6√(h² + k²)
So, RP/SP = 6√(h² + k²)/2√(h² + k²)
= 6/2
= 3
RP/RS = 6√(h² + k²)/8√(h² + k²)
= 6/8
= 3/4