Question

tw has a midpoint at (-3,-4). if t has coordinates (-6,-9), find the coordinates of n. t(-6,-9) n(?,?) multiple - choice question the endpoint n in this example in on the y - axis. true false

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $T(-6,-9)$ as $(x_1,y_1)$ and mid - point $(-3,-4)$ as $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=-3$. Substitute $x_1=-6$ into the equation: $\frac{-6 + x_2}{2}=-3$. Multiply both sides by 2: $-6 + x_2=-6$. Add 6 to both sides: $x_2 = 0$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=-4$. Substitute $y_1=-9$ into the equation: $\frac{-9 + y_2}{2}=-4$. Multiply both sides by 2: $-9 + y_2=-8$. Add 9 to both sides: $y_2 = 1$.

Answer:

The coordinates of $N$ are $(0,1)$