I will be using a practice problem with different endpoints, and I challenge you to solve this one using a similar strategy. The points I will be using is
(1, 3) as T and (5, 4) as the midpoint
Alright - we know that the equation for the midpoint of a line segment is
[tex]( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} )[/tex]
Next, we plug the x values in - since the midpoint's x value is 5 and one endpoint's x value is 1, we have
[tex] \frac{1+x_2}{2} =5[/tex] .
Next, we multiply both sides by 2, resulting in 1+x₂=10. Lastly, we subtract 1 from both sides, meaning that x₂, or the x value of the other endpoint, is 9. For the y values, we use a similar process -
[tex] \frac{3+y_2}{2} =4[/tex] .
since 3 is the y value of one endpoint and 4 is the y value of the midpoint. Multiplying both sides by 2, we get 3+y₂=8. Subtracting 3 from both sides, we get y₂=5 and our coordinates for the other endpoint to be (9, 5).
Good luck, and feel free to ask any questions as necessary!
