Question

The midpoint of the line segment from upper p 1p1 to upper p 2p2 is left parenthesis negative 1 comma 5 right parenthesis(−1,5). if upper p 1p1equals=left parenthesis negative 4 comma 6 right parenthesis(−4,6)​, what is upper p 2 question mark p2?

Answer 1

The coordinates of the second point are (2, 4).

The midpoint formula is:

`m=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Substituting our information, we have:


`(-1, 5)=((-4+x_2)/(2),(6+y_2)/(2))`

This means that

`-1=(-4+x_2)/(2) \text{ and } 5=(6+y_2)/(2)`

Multiply both sides of both equations by 2 to cancel it:

`-1*2=((-4+x_2)/(2))*2 \text { and } 5*2=((6+y_2)/(2))*2 \\ \\-2=-4+x_2 \text { and } 10=6+y_2 \\-2+4=-4+x_2+4 \text { and } 10-6=6+y_2-6 \\2=x_2 \text{ and } 4=y_2`

This gives us our coordinates (2, 4)