Indicate the equation of the given line in standard form The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).

The answer to your question is  13x - 9y = 135/2

Step-by-step explanation:

Data

R (-1, 5)

S (1, 8)

T (7 , -2)

U (2, 0)

Process

1.- Plot the points

See the graph below

2.- Determine the midpoints of RS and TU

RS       Xm = (-1 + 1)/2 = 0/2 = 0

           Ym = (5 + 8)/2 = 13/2 = 6.5

            (0, 6.5)

TU       Xm = (7 + 2)/2 = 9/2 = 4.5

          Ym = (-2 + 0)/2 = -2/2 = -1

            (4.5, -1)

3.- Calculate the slope

         m = (-1 - 6.5)/(4.5 - 0) = -7.5/4.5 = 13/9

4.- Find the equation of the median

        y + 1 = 13/9(x - 9/2)

        9(y + 1) = 13(x - 9/2)

        9y + 9 = 13x - 117/2

        13x - 9y = 9 + 117/2

        13x - 9y = 135/2

answer: it is d

step-by-step explanation: