AA, BBB, and CCC are collinear, and BBB is between AAA and CCC. The ratio of ABABA, B to BCBCB, C is 1:21:21, colon, 2. If AAA is at (7,-1)(7,−1)left parenthesis, 7, comma, minus, 1, right parenthesis and BBB is at (2,1)(2,1)left parenthesis, 2, comma, 1, right parenthesis, what are the coordinates of point CCC?
Accepted Solution
A:
Answer:The coordinates of point C are (-8,5).Step-by-step explanation:It is given that A, B and C collinear and B is between A and C.The ratio of AB to BC is 1:2. It means Point divided the line segments AC in 1:2.Section formula:[tex](\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})[/tex]The given points are A(7,-1) and B(2,1).Let the coordinates of C are (a,b).Using section formula the coordinates of B are[tex]B=(\dfrac{(1)(a)+(2)(7)}{1+2},\dfrac{(1)(b)+(2)(-1)}{1+2})[/tex][tex]B=(\dfrac{a+14}{3},\dfrac{b-2}{3})[/tex]We know that point B(2,1).[tex](2,1)=(\dfrac{a+14}{3},\dfrac{b-2}{3})[/tex]On comparing both sides we get[tex]2=\dfrac{a+14}{3}[/tex][tex]6=a+14[/tex][tex]6-14=a[/tex][tex]-8=a[/tex]The value of a is -8.[tex]1=\dfrac{b-2}{3}[/tex][tex]3=b-2[/tex][tex]3+2=b[/tex][tex]5=b[/tex]The value of b is 5.Therefore, the coordinates of point C are (-8,5).