Question

the midpoint m of $overline{uv}$ has coordinates (2.7, 5.8). point v has coordinates (-8.3, 7.4). find the coordinates of point u. write the coordinates as decimals or integers. u = ( , )

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 the coordinates of point $U$ be $(x,y)$ and the coordinates of point $V$ be $(-8.3,7.4)$ and the mid - point $M$ be $(2.7,5.8)$.

Step2: Solve for the x - coordinate of U

We have $\frac{x+( - 8.3)}{2}=2.7$. Multiply both sides by 2: $x - 8.3=2.7\times2$. Then $x-8.3 = 5.4$. Add 8.3 to both sides: $x=5.4 + 8.3=13.7$.

Step3: Solve for the y - coordinate of U

We have $\frac{y + 7.4}{2}=5.8$. Multiply both sides by 2: $y+7.4=5.8\times2$. Then $y + 7.4=11.6$. Subtract 7.4 from both sides: $y=11.6 - 7.4 = 4.2$.

Answer:

$(13.7,4.2)$