Question

the midpoint of a line segment is (6, 5), and one of the endpoints is (3, 6). what are the coordinates of the other endpoint?
a. (3, 4)
b. (5, 8)
c. (9, 3)
d. (18.3, 6.3)

Explanation:

Step1: Use the 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 the mid - point \(M=(6,5)\) and one endpoint \((x_1,y_1)=(1,6)\). We need to find \((x_2,y_2)\).
For the \(x\) - coordinate: \(\frac{x_1+x_2}{2}=6\), substituting \(x_1 = 1\) gives \(\frac{1 + x_2}{2}=6\). Cross - multiply: \(1+x_2=12\), so \(x_2=11\).
For the \(y\) - coordinate: \(\frac{y_1 + y_2}{2}=5\), substituting \(y_1 = 6\) gives \(\frac{6 + y_2}{2}=5\). Cross - multiply: \(6+y_2 = 10\), so \(y_2=4\).

Answer:

A. \((11,4)\)