andrewlibylina
contestada

[100POINTS)A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work.


Please answer this in the most simplest way for me to understand.

Thank you.

I

Respuesta :

evgeniylevi

Answer:

[tex]\frac{41}{11}.[/tex]

Step-by-step explanation:

1) to make up the equation of the given line:

[tex]\frac{x-X_R}{X_S-X_R} =\frac{y-Y_R}{Y_S-Y_R}; \ => \frac{x+5}{1+5} =\frac{y+6}{5+6}; \ => \frac{x+5}{6} =\frac{y+6}{11}.[/tex]

2) to substitute y=10 into the equation of the given line, then to calculate the value of 'x':

[tex]\frac{x+5}{6} =\frac{10+6}{11}; \ => \ x=\frac{96}{11}-5=\frac{41}{11}.[/tex]

Equation of ST :-

Slope=

  • m=5+6/1+5=11/6

Equation in point slope form

  • y+6=11/6(x+5)
  • 6y+36=11x+55
  • 6y=11x+19
  • y=11/6x+19/6

Now T lies on this line

  • 10=11/6x+19/6

Ok solving we would get

  • x=41/11

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