Question

1. midpoint of mn is (2,-3) and n is (-4,5). what are the coordinates of m?

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points \(M(x_1,y_1)\) and \(N(x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(M=(x,y)\) and \(N=(-4,5)\), and mid - point \(P=(2,-3)\).
So, \(\frac{x+( - 4)}{2}=2\) and \(\frac{y + 5}{2}=-3\).

Step2: Solve for \(x\)

From \(\frac{x-4}{2}=2\), multiply both sides by \(2\): \(x - 4=4\). Then add \(4\) to both sides: \(x=4 + 4=8\).

Step3: Solve for \(y\)

From \(\frac{y + 5}{2}=-3\), multiply both sides by \(2\): \(y+5=-6\). Then subtract \(5\) from both sides: \(y=-6 - 5=-11\).

Answer:

\((8,-11)\)