P₂ = (-3, 10)
Explanation:The midpoint, (a, b) = (-5, 3)
The starting point, P₁ = (x₁, y₁) = (-7, 4)
Let P₂ = (x₂, y₂)
The formulae for the coordinates of the midpoint are:
[tex]\begin{gathered} a=\frac{x_1+x_2}{2} \\ b=\frac{y_1+y_2}{2} \end{gathered}[/tex]To solve for x₂, substitute a = -5, x₁ = -7 into the formula
[tex]\begin{gathered} -5=\frac{-7+x_2}{2} \\ -5(2)=-7+x_2 \\ -10=-7+x_2 \\ x_2=-10+7 \\ x_2=-3 \end{gathered}[/tex]To solve for y₂, substitute b = 3, y₁ = -4 into the formula
[tex]\begin{gathered} b=\frac{y_1+y_2}{2} \\ 3=\frac{-4+y_2}{2} \\ 2(3)=-4+y_2 \\ 6=-4+y_2 \\ y_2=6+4 \\ y_2=10 \\ \end{gathered}[/tex]Therefore, P₂ = (-3, 10)
