The midpoint of line AB has coordinates of (5,-1). If the coordinates of A are (2,-3), what are the coordinates of B?
Any help is appreciated!
ok now please solve my geometric problem please
A(2 , -3) , M(5 , -1) , B(X , Y).
X - 2 = 2(5 - 2),
X - 2 = 6,
X = 6 + 2 = 8.
Y-(-3) = 2(-1 - (-3)),
Y + 3 = 4,
Y = 4 - 3 = 1.
B(8 , 1).
If the midpoint of line segment AB has coordinates (1,-3) and A= (-9,8) then what is the coordinates of B?
Well, since the midpoint of line AB is at (5,-1), we can use the formula for the midpoint to find the coordinates of point B. The formula is ( (x1+x2)/2, (y1+y2)/2 ).
So, let's plug in the given coordinates of the midpoint and point A:
x1 = 2
y1 = -3
x2 = B (we don't know yet)
y2 = B (we don't know yet)
Using the formula, we get:
( (2+x2)/2, (-3+y2)/2 ) = (5,-1)
Now, we can solve for x2 and y2:
(2+x2)/2 = 5
2+x2 = 10
x2 = 8
and
(-3+y2)/2 = -1
-3+y2 = -2
y2 = -1
So, the coordinates of point B are (8, -1).
I hope that helps!
To find the coordinates of point B, we can use the formula for the midpoint of a line segment. The midpoint formula states that the coordinates of the midpoint (M) between two points (A and B) can be found by taking the average of their x-coordinates and the average of their y-coordinates.
Given that the x-coordinate of the midpoint M is 5 and the x-coordinate of point A is 2, we can calculate the x-coordinate of point B as follows:
X-coordinate of B = 2 * X-coordinate of M - X-coordinate of A
Substituting the values we have:
X-coordinate of B = 2 * 5 - 2 = 10 - 2 = 8
Next, let's calculate the y-coordinate of point B. Given that the y-coordinate of the midpoint M is -1 and the y-coordinate of point A is -3, we can use the same formula to find the y-coordinate of point B:
Y-coordinate of B = 2 * Y-coordinate of M - Y-coordinate of A
Substituting the values we have:
Y-coordinate of B = 2 * (-1) - (-3) = -2 + 3 = 1
So, the coordinates of point B are (8, 1).