Question

the midpoint of tu is m(10, 5.5). one endpoint is t(0, 99). find the coordinates of the other endpoint 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 $T(x_1,y_1)=(0,99)$ and $U(x_2,y_2)$. The mid - point $M(x_m,y_m)=(10,5.5)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, $10=\frac{0 + x_2}{2}$. Cross - multiply: $10\times2=0 + x_2$, so $x_2 = 20$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, $5.5=\frac{99 + y_2}{2}$. Cross - multiply: $5.5\times2=99 + y_2$, so $11=99 + y_2$. Then $y_2=11 - 99=-88$.

Answer:

$(20,-88)$