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if the coordinates of r are (4, 7) and the midpoint of RS is (0, 5 ), what are the coordinates of s?

Sagot :

To solve this problem, we recall that the formula for the coordinates of the midpoint between (x₁,y₁), and (x₂,y₂) is:

[tex]\begin{gathered} x=\frac{x_1+x_2}{2}, \\ y=\frac{y_1+y_2}{2}. \end{gathered}[/tex]

Substituting the given coordinates for the midpoint and one of the terminal points, we get:

[tex]\begin{gathered} 0=\frac{4+s_x}{2}, \\ 5=\frac{7+s_y}{2}. \end{gathered}[/tex]

Solving the above equations for s_x, and s_y, we get:

[tex]\begin{gathered} s_x=0*2-4, \\ s_y=5*2-7. \end{gathered}[/tex]

Finally, we get that the coordinates of s are:

[tex](-4,3).[/tex]

Answer:

[tex](-4,3).[/tex]