Answer:
(7, 5)
Step-by-step explanation:
If point C is the midpoint of the line segment AB, we can use the midpoint formula to find the coordinates of point B.
The midpoint formula states that if the coordinates of the endpoints of a line segment are [tex](x_1, y_1) [/tex] and [tex] (x_2, y_2)[/tex] , then the coordinates of the midpoint (M) are given by:
[tex] \Large\boxed{\boxed{ M = \left( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \right)}} [/tex]
Given that point A is at (1, 1) and point C is at (4, 3), and point C is the midpoint, we can use the midpoint formula to find the coordinates of point B.
Let the coordinates of point B be (x, y).
Using the midpoint formula:
[tex] \left( \dfrac{1 + x}{2}, \dfrac{1 + y}{2} \right) = (4, 3) [/tex]
Now, we can equate the x-coordinates and the y-coordinates:
For the x-coordinates:
[tex] \dfrac{1 + x}{2} = 4 [/tex]
[tex] 1 + x = 2 \times 4 [/tex]
[tex] 1 + x = 8 [/tex]
[tex] x = 8 - 1 [/tex]
[tex] x = 7 [/tex]
For the y-coordinates:
[tex] \dfrac{1 + y}{2} = 3 [/tex]
[tex] 1 + y = 2 \times 3 [/tex]
[tex] 1 + y = 6 [/tex]
[tex] y = 6 - 1 [/tex]
[tex] y = 5 [/tex]
Therefore, the coordinates of point B are (7, 5).
