Question

find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: let (x,y) be the unknown endpoint. apply the midpoint formula, and solve the two equations for x and y.) midpoint (15, - 10), endpoint (19, - 2) the other endpoint is (type an ordered pair.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $(x_1,y_1)=(x,y)$ (the unknown endpoint), $(x_2,y_2)=(19, - 2)$ and the mid - point $(m_x,m_y)=(15,-10)$.

Step2: Solve for x - coordinate

We know that $m_x=\frac{x_1 + x_2}{2}$. Substituting the values, we get $15=\frac{x + 19}{2}$. Cross - multiply: $15\times2=x + 19$, so $30=x + 19$. Then $x=30 - 19=11$.

Step3: Solve for y - coordinate

We know that $m_y=\frac{y_1 + y_2}{2}$. Substituting the values, we get $-10=\frac{y+( - 2)}{2}$. Cross - multiply: $-10\times2=y - 2$, so $-20=y - 2$. Then $y=-20 + 2=-18$.

Answer:

$(11,-18)$