Question

1. rt has an endpoint r at (4, 4) and a midpoint at (1, -2). what is the coordinate of the other endpoint? (draw a table)

t = ( )

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

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $1=\frac{4 + x_2}{2}$. 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 values, we have $-2=\frac{4 + y_2}{2}$. Cross - multiply: $-4 = 4+y_2$. Then $y_2=-4 - 4=-8$.

Answer:

$(-2,-8)$