Three vertices of parallelogram PRTV are P(-4,-4), R(-10,0), and V(5,-1). Find the coordinates of vertex T.
1 answer:
Slope of TV = Slope of PR (y + 1)/(x - 5) = (0 + 4)/(-10 + 4) (y + 1)/(x - 5) = -4/6 6(y + 1) = -4(x - 5) 6y + 6= -4x + 20 equation #1: 6y + 4x = 14 Slope of RT = Slope of PV (y - 0)/(x + 10) = (-1 + 4)/(5 + 4) (y - 0)/(x + 10) = 3/9 3(y - 0) = 9(x + 10) 3y = 9x +90 equation #2: 3y = 9x +90 <span>We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix) to solve for the x and y coordinates. </span> equation #1: 6y + 4x = 14 equation #2: 3y - 9x = 90 Multiply equation 2 by -2 equation #1: 6y + 4x = 14 equation #2: -6y + 18x = -180 Add together Eq. 1 & 2 22x = -166 x = -7.5 6y +4(-7.5) = 14 6y = 44 y = 7 1/3 (-7 1/2, 7 1/3)
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