Question

determine a line segment with given midpoint. (4,4) mid point and segment determined by (1,2) and (a,b) i needa find (a,b)

Answer 1

Given:

A line segment with a midpoint = (4, 4)

The segment has the endpoints (1,2) and (a,b)

We will find the point (a, b) using the following formula:

`M=(P+Q)/(2)`

Where M is the midpoint of the line segment PQ

So, we can write the following equation:

`(4,4)=((1,2)+(a,b))/(2)`

Solve for (a, b) as follows:

`\begin{gathered} 2*(4,4)=(1,2)+(a,b) \\ (8,8)=(1+a,2+b) \\ \\ 1+a=8\to a=8-1=7 \\ 2+b=8\to b=8-2=6 \\ \\ (a,b)=(7,6) \end{gathered}`

So, the answer will be (a,b) = (7,6)