Question

1. if a line has a midpoint of m (20, 10) and an endpoint of a (5, 6), what are the coordinates of the other endpoint, b?

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $A(5,6)$ and $M(20,10)$, let the coordinates of $B$ be $(x,y)$.

Step2: Solve for $x$ - coordinate of $B$

We know that $\frac{5 + x}{2}=20$. Multiply both sides by 2: $5 + x=40$. Then subtract 5 from both sides: $x = 40-5=35$.

Step3: Solve for $y$ - coordinate of $B$

We know that $\frac{6 + y}{2}=10$. Multiply both sides by 2: $6 + y=20$. Then subtract 6 from both sides: $y=20 - 6 = 14$.

Answer:

$(35,14)$