M \left(-1,5\right) is the midpoint of AB If A has coordinates \left(4,3\right) Find the x coordinate of B. (Use the variable x in your working out, Find the y coordinate of B.
(Use the variable y in your working out)
To find the x-coordinate of point B, we can use the midpoint formula:
Midpoint formula: M(x_m, y_m) = ((x_1 + x_2)/2, (y_1 + y_2)/2)
Given that M(-1, 5) is the midpoint of AB, and A has coordinates (4, 3), we can plug in the known values into the formula:
-1 = (4 + x_2)/2
Multiplying both sides by 2 gives us:
-2 = 4 + x_2
Subtracting 4 from both sides gives us:
-2 - 4 = x_2
Simplifying gives us:
x_2 = -6
Therefore, the x-coordinate of point B is -6.
To find the y-coordinate of point B, we can use the same formula:
5 = (3 + y_2)/2
Multiplying both sides by 2 gives us:
10 = 3 + y_2
Subtracting 3 from both sides gives us:
10 - 3 = y_2
Simplifying gives us:
y_2 = 7
Therefore, the y-coordinate of point B is 7.
So, the coordinates of point B are (-6, 7).