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 for x and y.) midpoint (10,18), endpoint (17,12) 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), $(x_2,y_2)=(17,12)$ and the mid - point $(m_x,m_y)=(10,18)$.

Step2: Solve for x

We know that $m_x=\frac{x_1 + x_2}{2}$. Substituting the values, we get $10=\frac{x + 17}{2}$. Cross - multiply: $2\times10=x + 17$, so $20=x + 17$. Then $x=20 - 17=3$.

Step3: Solve for y

We know that $m_y=\frac{y_1 + y_2}{2}$. Substituting the values, we get $18=\frac{y + 12}{2}$. Cross - multiply: $2\times18=y + 12$, so $36=y + 12$. Then $y=36 - 12 = 24$.

Answer:

$(3,24)$