Question

The line segment AB is divided into five congruent parts at P, Q, R and S such that A-P-Q-R-S-B. If point Q(12,14) and S(4,18) are given find the coordinates of A, P, R,B.

Answer 1

Steps:
1) We have , line segment AB which is divided into equal parts. 
Given: Q (12,14) 
               S=(4,18) 
Since, $R(x_{3},y_{3})$ divides QS into two equal parts. 
$=\ \textgreater \ R(x_{3},y_{3})= ( \frac{12+4}{2} , \frac{14+18}{2}) =(8,16)$

2) Similarly,S divides RB into two equal parts :  $B(x_{4},y_{4})$ 

$S(4,18) = ( \frac{8+x_{4}}{2} , \frac{16+y_{4}}{2}) \\ \\ =\ \textgreater \ B(x_{4},y_{4}) = (0,20)$

3) Similarly, Q divides PR into two equal parts ;$P(x_{2},y_{2})$
  
$=\ \textgreater \ Q(12,14) = ( \frac{x_{2}+18}{2}, \frac{y_{4}+16}{2}) \\ \\ =\ \textgreater \ P(x_{2},y_{2}) = (6,12)$

4) Similarly, P divides AQ into two equal parts ; $A(x_{1},y_{1})$ 
[tex]=\ \textgreater \ (6,12) = ( \frac{x_{1}+12}{2}, \frac{y_{1}+14}{2}) \\ \\ =\ \textgreater \ A(x_{1},y_{1}) = (0,10) [/tex]

Hence , we obtained all required points . 

Answer 2

1. Step-by-step explanation:
2. Step-by-step explanation:Answers in the picture