Question

1. m is the mid - point of ab, find the coordinates of a if m(-3, 1) and b(2, 0)
2. m is the mid - point of dc, find the coordinates of a if m(-4, 2) and c(6, 2)

Explanation:

Step1: Recall mid - point formula

Let \(M(x_m,y_m)\) be the mid - point of the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\), then \(x_m=\frac{x_1 + x_2}{2}\) and \(y_m=\frac{y_1 + y_2}{2}\).

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

Given \(M(-3,1)\), \(B(2,0)\). For \(x\) - coordinate: \(-3=\frac{x_A + 2}{2}\), so \(x_A=-6 - 2=-8\). For \(y\) - coordinate: \(1=\frac{y_A+0}{2}\), so \(y_A = 2\).

Step3: Solve for \(x\) - coordinate of \(A\) in second case

Given \(M(-4,2)\), \(C(6,2)\). For \(x\) - coordinate: \(-4=\frac{x_A + 6}{2}\), so \(x_A=-8 - 6=-14\). For \(y\) - coordinate: \(2=\frac{y_A + 2}{2}\), so \(y_A=2\).

Answer:

1. \(A(-8,2)\)
2. \(A(-14,2)\)