Question

determining endpoints in exercises 41 - 44, you are given an endpoint and the midpoint of a line segment. find the coordinates of the other endpoint. each midpoint is denoted by m(x, y). (review 1.5 for 2.5)

1. b(5, 7)

m(-1, 0)

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 $B(5,7)$ be $(x_1,y_1)$ and the unknown endpoint be $(x_2,y_2)$, and $M(-1,0)$.

Step2: Find the x - coordinate of the unknown endpoint

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 5$ and $x_M=-1$ into the formula: $\frac{5 + x_2}{2}=-1$. Multiply both sides by 2: $5 + x_2=-2$. Then subtract 5 from both sides: $x_2=-2 - 5=-7$.

Step3: Find the y - coordinate of the unknown endpoint

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 7$ and $y_M = 0$ into the formula: $\frac{7 + y_2}{2}=0$. Multiply both sides by 2: $7 + y_2=0$. Then subtract 7 from both sides: $y_2=-7$.

Answer:

$(-7,-7)$