The midpoint of line segment AB is (1, −3)
. Point A is at (−3, 4)
. Find point B.(1 point)
Responses
(7, -8)
(7, -8)
(-10, 5)
(-10, 5)
(-8, 7)
(-8, 7)
(5, -10)
(5, -10)
To find point B, we can use the midpoint formula:
Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint of line segment AB is (1, -3) and the coordinates of point A are (-3, 4), we can substitute these values into the formula:
(1, -3) = ((-3 + x2)/2, (4 + y2)/2)
Simplifying further:
-3 = (-3 + x2)/2 (Equation 1)
1 = (4 + y2)/2 (Equation 2)
To solve for x2, we multiply both sides of equation 1 by 2:
-6 = -3 + x2
Adding 3 to both sides:
-3 = x2
So, x-coordinate of point B is -3.
To solve for y2, we multiply both sides of equation 2 by 2:
2 = 4 + y2
Subtracting 4 from both sides:
-2 = y2
So, y-coordinate of point B is -2.
Therefore, the coordinates of point B are (-3, -2).
To find the coordinates of point B, you can use the formula for finding the midpoint of a line segment. The midpoint formula is given by:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
In this case, we are given that the midpoint of line segment AB is (1, -3) and the coordinates of point A are (-3, 4). Let's plug in these values into the midpoint formula to find the coordinates of point B.
Let's set up the equation:
[(x1 + x2)/2, (y1 + y2)/2] = (1, -3)
Plugging in the known values:
[(-3 + x2)/2, (4 + y2)/2] = (1, -3)
Now, solve for x2 and y2:
-3 + x2 = 2
x2 = 2 + 3 = 5
4 + y2 = -6
y2 = -6 - 4 = -10
Therefore, the coordinates of point B are (5, -10).