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:
$m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Substituting our information, we have:

$(-1, 5)=(\frac{-4+x_2}{2},\frac{6+y_2}{2})$

This means that
$-1=\frac{-4+x_2}{2} \text{ and } 5=\frac{6+y_2}{2}$

Multiply both sides of both equations by 2 to cancel it:
$-1\times2=(\frac{-4+x_2}{2})\times2 \text { and } 5\times2=(\frac{6+y_2}{2})\times2 \\ \\-2=-4+x_2 \text { and } 10=6+y_2 \\-2+4=-4+x_2+4 \text { and } 10-6=6+y_2-6 \\2=x_2 \text{ and } 4=y_2$

This gives us our coordinates (2, 4)