Question

st has a mid - point at m(-4.5, 0). point s is at (-4, -4). find the coordinates of point t. write the coordinates as decimals or integers. t = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $S(x_1,y_1)=(-4,-4)$ and $T(x_2,y_2)$, and $M(-4.5,0)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-4.5$. Substitute $x_1=-4$ into the equation: $\frac{-4 + x_2}{2}=-4.5$. Multiply both sides by 2: $-4+x_2=-9$. Then add 4 to both sides: $x_2=-9 + 4=-5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=0$. Substitute $y_1=-4$ into the equation: $\frac{-4 + y_2}{2}=0$. Multiply both sides by 2: $-4+y_2=0$. Then add 4 to both sides: $y_2 = 4$.

Answer:

$(-5,4)$