Question

the midpoint of cd is m=(1,3). one endpoint is c=(4,5). find the coordinates of the other endpoint, d.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(C(x_1,y_1)\) and \(D(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(C(4,5)\) and \(M(1,3)\), for the \(x\) - coordinate of the mid - point: \(\frac{4 + x_2}{2}=1\), and for the \(y\) - coordinate: \(\frac{5 + y_2}{2}=3\).

Step2: Solve for \(x\) - coordinate of \(D\)

Solve the equation \(\frac{4 + x_2}{2}=1\). Multiply both sides by 2: \(4 + x_2=2\). Then subtract 4 from both sides: \(x_2=2 - 4=-2\).

Step3: Solve for \(y\) - coordinate of \(D\)

Solve the equation \(\frac{5 + y_2}{2}=3\). Multiply both sides by 2: \(5 + y_2 = 6\). Then subtract 5 from both sides: \(y_2=6 - 5 = 1\).

Answer:

\((-2,1)\)