Answer:
The coordinates of the other end is [tex](16,2)[/tex]
Step-by-step explanation:
Given
[tex]End 1: (-6,2)[/tex]
[tex]Midpoint: (5,2)[/tex]
Required
Find the coordinates of the other end
Let Midpoint be represented by (x,y);
(x,y) = (5,2) is calculated as thus
[tex](x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
So
[tex]x = \frac{x_1 + x_2}{2}[/tex] and [tex]y = \frac{y_1 + y_2}{2}[/tex]
Where [tex](x_1,y_1) = (-6,2)[/tex] and [tex](x,y) = (5,2)[/tex]
So, we're solving for [tex](x_2,y_2)[/tex]
Solving for [tex]x_2[/tex]
[tex]x = \frac{x_1 + x_2}{2}[/tex]
Substitute 5 for x and -6 for x₁
[tex]5 = \frac{-6 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 5 = \frac{-6 + x_2}{2} * 2[/tex]
[tex]10 = -6 + x_2[/tex]
Add 6 to both sides
[tex]6 + 10 = -6 +6 + x_2[/tex]
[tex]x_2 = 16[/tex]
Solving for [tex]y_2[/tex]
[tex]y = \frac{y_1 + y_2}{2}[/tex]
Substitute 2 for y and 2 for y₁
[tex]2 = \frac{2 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 2 = \frac{2 + y_2}{2} * 2[/tex]
[tex]4 = 2 + y_2[/tex]
Subtract 2 from both sides
[tex]4 - 2 = 2 - 2 + y_2[/tex]
[tex]y_2 = 2[/tex]
[tex](x_2,y_2) = (16,2)[/tex]
Hence, the coordinates of the other end is [tex](16,2)[/tex]
