Question

1. the midpoint of xy is m(1, 2). one endpoint is x(4, 1). find the coordinates of endpoint y.

how did he find this endpoint?
multiple - choice question
he used the slope to rise/run in the opposite direction.
he plugged numbers into an equation.

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 one endpoint $X=(x_1,y_1)=(4,1)$ and the mid - point $M=(x_m,y_m)=(1,2)$. Let the other endpoint be $Y=(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the given values: $1=\frac{4 + x_2}{2}$. Cross - multiply: $2=4 + x_2$. Then $x_2=2 - 4=-2$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the given values: $2=\frac{1 + y_2}{2}$. Cross - multiply: $4=1 + y_2$. Then $y_2=4 - 1 = 3$.

Answer:

The coordinates of endpoint $Y$ are $(-2,3)$