Question

1. fill in the blanks using the available answer choices. find the coordinates of a if m(6, -1) is the mid - point of ab, and b has the coordinates (8, -7). the coordinates of a are (blank 1, blank 2).

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(M(6,-1)\) and \(B(8,-7)\), let the coordinates of \(A\) be \((x,y)\). Then \(\frac{x + 8}{2}=6\) and \(\frac{y+( - 7)}{2}=-1\).

Step2: Solve for \(x\)

Solve the equation \(\frac{x + 8}{2}=6\). Multiply both sides by 2: \(x + 8=12\). Subtract 8 from both sides: \(x=12 - 8=4\).

Step3: Solve for \(y\)

Solve the equation \(\frac{y-7}{2}=-1\). Multiply both sides by 2: \(y - 7=-2\). Add 7 to both sides: \(y=-2 + 7 = 5\).

Answer:

\((4,5)\)