Answer:
[tex](-2,6)[/tex]
Step-by-step explanation:
Given
[tex]Elena = (10,-4)[/tex]
[tex]Midpoint = (4,1)[/tex]
Required
Determine the coordinates of Naya's
Midpoint is calculated as:
[tex]M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]
In this case:
[tex](x_1,y_1) = (10,-4)[/tex]
[tex](x,y) = (4,1)[/tex]
So, we have:
[tex](4,1) = \frac{1}{2}(10+x_2,-4+y_2)[/tex]
Multiply through by 2
[tex]2 * (4,1) = \frac{1}{2}(10+x_2,-4+y_2) * 2[/tex]
[tex](8,2) = (10+x_2,-4+y_2)[/tex]
By comparison:
[tex]8 = 10 + x_2[/tex]
[tex]2 = -4 + y_2[/tex]
So:
[tex]8 = 10 + x_2[/tex]
[tex]x_2 = 8 - 10[/tex]
[tex]x_2 = -2[/tex]
[tex]2 = -4 + y_2[/tex]
[tex]y_2 =2+4[/tex]
[tex]y_2 =6[/tex]
So, the coordinate is: [tex](-2,6)[/tex]
