Solution:
Keep in mind ,
Equation of line joining two points (a,b) and (p,q) is given by :
[tex]\frac{q-b}{p-a}=\frac{y-b}{x-a}[/tex]
Equation of line P which is obtained by joining (- 8,15) and (6, - 12) is given by:
[tex]\frac{y-15}{x+8}=\frac{-12-15}{6+8}\\\\ 14(y-15)=-27(x+8)\\\\ 14 y -210= -27 x - 216\\\\ 27 x+14 y+6=0[/tex]
Equation of line Q which is obtained by joining (4,16) and (-9, 10) is given by:
[tex]\frac{y-16}{x-4}=\frac{16-10}{4+9}\\\\ 13(y-16)=6(x-4)\\\\ 13 y -208= 6 x - 24\\\\ 6 x-13 y+184=0[/tex]
Equation of line P and Q are
27 x+14 y+6=0-------(1)× 2
6 x-13 y+184=0-------(2)× 9
54 x + 2 8 y+12=0---(1)
54 x -117 y +1656=0----(2)
(1) - (2)
145 y= 1644
y=11.33,
27 x+14 y+6=0-------(1)×13
6 x-13 y+184=0-------(1)×14
351 x + 182 y + 78=0-----(1)
84 x - 182 y +2576=0----(2)
(1) + (2)
435 x + 2654=0
x = - 6.11
So, solution set is (-6.11, 11.33)
Option (C) is true. (−2, 4), because this point makes both the equations incorrect.
Answer:
(−2, 4), because it is the point of intersection of the two graphs
Step-by-step explanation:
