Question

question
the midpoint of ab is m(3, -5). if the coordinates of a are (5, -3), what are the coordinates of b?

Explanation:

Step1: Recall the midpoint formula

The midpoint formula for two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(A=(5,-3)\) and \(M=(3,-5)\), and \(B=(x,y)\).

Step2: Set up equations for \(x\) - coordinate

Using the \(x\) - coordinate of the midpoint formula: \(\frac{5 + x}{2}=3\).
Multiply both sides by 2: \(5 + x=6\).
Subtract 5 from both sides: \(x = 6-5=1\).

Step3: Set up equations for \(y\) - coordinate

Using the \(y\) - coordinate of the midpoint formula: \(\frac{-3 + y}{2}=-5\).
Multiply both sides by 2: \(-3 + y=-10\).
Add 3 to both sides: \(y=-10 + 3=-7\).

Answer:

The coordinates of \(B\) are \((1,-7)\)