Question

one endpoint of a segment is a(2, 2). the midpoint of the segment is o(4, 11). what are the coordinates of the other endpoint?
a (2, 2)
b (2, 9)
c (6, 13)
d (6, 20)
a
b
c
d

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let one endpoint \(A=(x_1,y_1)=(2,2)\) and mid - point \(D=(x,y)=(4,6)\). Let the other endpoint be \(B=(x_2,y_2)\).
We know that \(x=\frac{x_1 + x_2}{2}\) and \(y=\frac{y_1 + y_2}{2}\).
For the \(x\) - coordinate:
\(4=\frac{2 + x_2}{2}\)
Multiply both sides by \(2\): \(8 = 2+x_2\)
Subtract \(2\) from both sides: \(x_2=6\)
For the \(y\) - coordinate:
\(6=\frac{2 + y_2}{2}\)
Multiply both sides by \(2\): \(12 = 2+y_2\)
Subtract \(2\) from both sides: \(y_2 = 10\)

Answer:

B. \((6,10)\)