Question

uv has a midpoint at m(-2, 1.5). point u is at (14, 3). find the coordinates of point v. write the coordinates as decimals or integers. v = ( ) ( )

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 $U(x_1,y_1)=(14,3)$ and $V(x_2,y_2)$. The mid - point $M(-2,1.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1 = 14$ into the equation: $\frac{14 + x_2}{2}=-2$. Multiply both sides by 2: $14 + x_2=-4$. Then subtract 14 from both sides: $x_2=-4 - 14=-18$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1.5$. Substitute $y_1 = 3$ into the equation: $\frac{3 + y_2}{2}=1.5$. Multiply both sides by 2: $3 + y_2 = 3$. Then subtract 3 from both sides: $y_2=0$.

Answer:

$(-18,0)$