Question

1. find the other endpoint given midpoint and endpoint

b. the midpoint of xy is m(1, 2). one endpoint is x(4, 1). find the coordinates of endpoint y.
what are the coordinates of this endpoint?
multiple - choice question
(-2,3)
(1,2)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 $X(x_1,y_1)=(4,1)$ and $Y(x_2,y_2)=(x,y)$, and $M(1,2)$.

Step2: Solve for x - coordinate

We know that $\frac{4 + x}{2}=1$. Cross - multiply: $4 + x=2$. Then $x=2 - 4=-2$.

Step3: Solve for y - coordinate

We know that $\frac{1 + y}{2}=2$. Cross - multiply: $1 + y = 4$. Then $y=4 - 1 = 3$.

Answer:

$(-2,3)$