Question

What is the other endpoint if one endpoint is (10,12) and the midpoint is (6,9).?

Answer 1

Answer:

$(2,\, 6)$.

Step-by-step explanation:

Let $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ denote the two endpoints.

The formula for the midpoint of these two points would be:

$\displaystyle \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)$.

(Similar to taking the average of each coordinate.)

In this question, it is given that $x_{0} = 10$ whereas $y_{0} = 12$. Substitute these two values into the expression for the coordinate of the midpoint:

• $x$-coordinate of the midpoint: $\displaystyle \frac{10 + x_{1}}{2} = 6$.
• $y$-coordinate of the midpoint: $\displaystyle \frac{12 + y_{1}}{2} = 9$.

Solve these two equations for $x_{1}$ and $y_{1}$: $x_{1} = 2$ whereas $y_{1} = 6$.

Hence, the coordinate of the other point would be $(2,\, 6)$.