Answer:
[tex](4,3)[/tex]
Step-by-step explanation:
Given
[tex]R = (-2,-3)[/tex]
[tex]M = (1,0)[/tex]
Required
Determine the coordinates of S
Midpoint is calculated as:
[tex]M(x,y) = \frac{1}{2}(x_1 +x_2,y_1+y_2)[/tex]
Where:
[tex](x,y) = (1,0)[/tex]
[tex](x_1,y_1) = (-2,-3)[/tex]
Substitute these values in the above formula:
[tex](1,0) = \frac{1}{2}(-2 + x_2,-3+y_2)[/tex]
Multiply through by 2
[tex]2 * (1,0) = 2 * \frac{1}{2}(-2 + x_2,-3+y_2)[/tex]
[tex](2,0) = (-2 + x_2,-3+y_2)[/tex]
By direct comparison:
[tex]2 = -2 + x_2[/tex] and [tex]0 = -3 + y_2[/tex]
Solving for x2
[tex]2 = -2 + x_2[/tex]
[tex]x_2 = 2 + 2[/tex]
[tex]x_2 = 4[/tex]
Solving for y2
[tex]0 = -3 + y_2[/tex]
[tex]y_2 = 0 + 3[/tex]
[tex]y_2 = 3[/tex]
Hence, the coordinates of S is: [tex](4,3)[/tex]
