Question

a line segment has an endpoint at (4, 6). if the midpoint of the line segment is (1, 5), what is the location of the line segments other endpoint? (7, 7) (-0.5, 4.5) (2.5, 5.5) (-2, 4)

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 $(x_1,y_1)=(4,6)$ be one endpoint and $(x_m,y_m)=(1,5)$ be the mid - point. We want to find $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the 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 values, $5=\frac{6 + y_2}{2}$. Cross - multiply: $10=6 + y_2$. Then $y_2=10 - 6 = 4$.

Answer:

$(-2,4)$