Answer to Question #249689 in Analytic Geometry for Big

Question #249689

M is the midpoint of AC, find the coordinates of the missing endpoint

1 A(-9,6) and M(5, 1)

2 C(1,-8) and M (-8,-4)

Expert's answer

Midpoint formula:

"M(x,y) = \\frac{x_1+x_2}{2}, \\frac{y_1+y_2}{2}"

1.

"(5,1) = \\frac{-9+x_2}{2}, \\frac{6+y_2}{2} \\\\\n\n5 = \\frac{-9+x_2}{2} \\\\\n\n10 = -9 + x_2 \\\\\n\nx_2 = 19 \\\\\n\n1 = \\frac{6+y_2}{2} \\\\\n\n2 = 6+ y_2 \\\\\n\ny_2 = -4\n\nC =(19,-4)"

2.

"(-8,-4) = \\frac{x_1+1}{2}, \\frac{y_1-8}{2} \\\\\n\n-8 = \\frac{x_1+1}{2} \\\\\n\n-16 = x_1 + 1 \\\\\n\nx_1 = -17 \\\\\n\n-4 = \\frac{y_1-8}{2} \\\\\n\n-8 = y_1 -8 \\\\\n\ny_1=0 \\\\\n\nA = (-17,0)"