Question

the midpoint m of st has coordinates (5, 8.1). point s has coordinates (5.1, 10.7). 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 $S=(x_1,y_1)=(5.1,10.7)$ and $T=(x_2,y_2)$, and $M=(5,8.1)$.

Step2: Solve for the x - coordinate of T

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting the known values: $\frac{5.1+x_2}{2}=5$. Multiply both sides by 2: $5.1 + x_2=10$. Then subtract 5.1 from both sides: $x_2=10 - 5.1=4.9$.

Step3: Solve for the y - coordinate of T

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting the known values: $\frac{10.7+y_2}{2}=8.1$. Multiply both sides by 2: $10.7 + y_2=16.2$. Then subtract 10.7 from both sides: $y_2=16.2-10.7 = 5.5$.

Answer:

$(4.9,5.5)$