Question

el punto medio de $overline{pq}$ es $m = (-2, -4)$. uno de los puntos extremos es $p = (-4, -2)$. encontrar las coordenadas del otro punto extremo, $q$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(P(x_1,y_1)\) and \(Q(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(P(-4,-2)\) and \(M(-2,-4)\), let \(Q=(x,y)\).
For the x - coordinate of the mid - point: \(\frac{-4 + x}{2}=-2\).

Step2: Solve for x

Multiply both sides of \(\frac{-4 + x}{2}=-2\) by 2: \(-4 + x=-4\). Then add 4 to both sides: \(x = 0\).

Step3: Solve for y using the y - coordinate of the mid - point

For the y - coordinate of the mid - point: \(\frac{-2 + y}{2}=-4\). Multiply both sides by 2: \(-2 + y=-8\). Then add 2 to both sides: \(y=-6\).

Answer:

\((0,-6)\)