Final answer:
Using the midpoint formula, the coordinates of endpoint B are found to be (7, 6) by setting up equations for both x and y coordinates based on the given midpoint M(6,1) and point A(5,−4).
Step-by-step explanation:
The midpoint formula is used to find the coordinates of the midpoint M between two points A and B on the Cartesian plane. Given that the midpoint M(6,1) is exactly halfway between points A(5,−4) and B, which we are trying to find, we can set up an equation using the midpoint formula for both x and y coordinates.
For the x-coordinate of the midpoint: (x1 + x2) / 2 = 6, where x1 is the x-coordinate of A, which is 5. We can solve for x2, which is the x-coordinate of point B. Similarly, for the y-coordinate of the midpoint: (y1 + y2) / 2 = 1, where y1 is the y-coordinate of A, which is −4. Again, solving for y2 will give us the y-coordinate of point B.
Using the midpoint formula for the x-coordinates:
(5 + x2) / 2 = 6
5 + x2 = 12
x2 = 12 − 5
x2 = 7
For the y-coordinates:
(−4 + y2) / 2 = 1
−4 + y2 = 2
y2 = 2 + 4
y2 = 6
Therefore, the coordinates of endpoint B are (7, 6).