(-2.5, 7)
Explanations:The coordinates of the endpoint at A = (4.5, -3)
That is, (x₁, y₁) = (4.5, -3)
The coordinates of the midpoint at M = (1, 2)
That is, (a, b) = (1, 2)
Let the coordinates of the endpoint at B be represennted by (x₂, y₂)
The diagram representing the illustration is shown below:
The coordinates of the midpoint are given by the formulae:
[tex]\begin{gathered} a\text{ = }\frac{x_1+x_2_{}}{2} \\ b\text{ = }\frac{y_1_{}+y_2}{2} \end{gathered}[/tex]x₁ = 4.5, a = 1, solve for x₂
[tex]\begin{gathered} 1\text{ = }\frac{4.5+x_2}{2} \\ 2=4.5+x_2 \\ x_2=\text{ 2 - 4.5} \\ x_2=\text{ -2.5} \end{gathered}[/tex]y₁ = -3, b = 2, solve for y₂
[tex]\begin{gathered} 2\text{ = }\frac{-3+y_2}{2} \\ 4=-3+y_2 \\ y_2=\text{ 4 + 3} \\ y_2=\text{ 7} \end{gathered}[/tex]The coordinates, (x₂, y₂) = (-2.5, 7)
The location of the other endpoint B is B(-2.5, 7)
