4 Three collinear points on the coordinate plane are R(x, y), S(x + 8h, y + 8k), and P(+ + 6h, y + 6K)
RP
Part A: Determine the value of
SP
RP
Part B: Determine the value of

Please show the step you took to find the answer

RP/SP =3 , RP/RS = 3/4

Step-by-step 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

the answer is c. 23/3

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step-by-step explanation: