Question

find the coordinates of the missing endpoint if b is the midpoint of ac. c(-5,4), b(-2,5)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(A(x_1,y_1)\) and \(C(x_2,y_2)\) with mid - point \(B(x_m,y_m)\) is \(x_m=\frac{x_1 + x_2}{2}\) and \(y_m=\frac{y_1 + y_2}{2}\). Given \(C(-5,4)\), \(B(-2,5)\), let \(A=(x,y)\).

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

We know \(x_m=-2\), \(x_2=-5\). Using \(x_m=\frac{x_1 + x_2}{2}\), we substitute the values: \(-2=\frac{x+( - 5)}{2}\). Multiply both sides by 2: \(-4=x - 5\). Add 5 to both sides: \(x = 1\).

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

We know \(y_m = 5\), \(y_2=4\). Using \(y_m=\frac{y_1 + y_2}{2}\), we substitute the values: \(5=\frac{y + 4}{2}\). Multiply both sides by 2: \(10=y + 4\). Subtract 4 from both sides: \(y=6\).

Answer:

\(A(1,6)\)